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%!PS-Adobe-2.0 %%Creator: dvips(k) 5.92a Copyright 2002 Radical Eye Software %%Title: extDyn2.dvi %%Pages: 9 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX10 CMSY10 CMR8 CMCSC10 CMSY8 CMMI8 CMR6 CMR10 %%+ CMMI10 CMMI7 CMR7 CMMI5 MSBM10 CMSY7 CMR5 CMEX10 CMTI8 LCIRCLE10 %%+ LINE10 MSAM10 CMTI10 CMSY5 CMTT8 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o extDyn2.ps extDyn2.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2006.01.27:1519 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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cleartomark %%EndFont %%BeginFont: CMSY5 %!PS-AdobeFont-1.1: CMSY5 1.0 %%CreationDate: 1991 Aug 15 07:21:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{21 -944 1448 791}readonly def /UniqueID 5000815 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E3948FFB0B4E70F212EC976D65099D84E0D37A7A771C3101D6AD26A0513378F 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /square put dup 54 /lessorequalslant put dup 62 /greaterorequalslant put readonly def /FontBBox{8 -463 1331 1003}readonly def /UniqueID 5031981 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: LINE10 %!PS-AdobeFont-1.1: LINE10 1.001 %%CreationDate: 1992 Oct 23 20:22:05 %%RevisionDate: 2001 Jun 05 20:22:05 % Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.001) readonly def /Notice (Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved) readonly def /FullName (LINE10) readonly def /FamilyName (LaTeX) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /LINE10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 8 /a8 put dup 72 /a72 put readonly def /FontBBox{-150 -150 1020 1020}readonly def /UniqueID 5011940 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: LCIRCLE10 %!PS-AdobeFont-1.1: LCIRCLE10 1.001 %%CreationDate: 1992 Oct 23 20:21:59 %%RevisionDate: 2001 Jun 05 20:21:59 % Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.001) readonly def /Notice (Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved) readonly def /FullName (LCIRCLE10) readonly def /FamilyName (LaTeX) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /LCIRCLE10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 113 /a113 put dup 115 /a115 put readonly def /FontBBox{-2000 -2000 2040 2040}readonly def /UniqueID 5011942 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI8 %!PS-AdobeFont-1.1: CMTI8 1.0 %%CreationDate: 1991 Aug 18 21:07:42 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-35 -250 1190 750}readonly def /UniqueID 5000826 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 525003F3DAD7933EB57E7DB1462E9D906F6D8F5BF740206C1EC5F36E00AAFF68 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All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 2 /bracketleftbig put dup 3 /bracketrightbig put dup 8 /braceleftbig put dup 9 /bracerightbig put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 34 /bracketleftBigg put dup 35 /bracketrightBigg put dup 80 /summationtext put dup 88 /summationdisplay put dup 91 /uniondisplay put dup 110 /braceleftBig put dup 111 /bracerightBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueID 5000788 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 63 /emptyset put dup 67 /C put dup 78 /N put dup 82 /R put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueID 5087380 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF5B8CABB9FFC6CC3F1E9AE32F234EB60FE7D E34995B1ACFF52428EA20C8ED4FD73E3935CEBD40E0EAD70C0887A451E1B1AC8 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%%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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y(neither)j(a)g(Dynkin)h(graph)e(nor)h(an)g (extended)h(graph)e(then)i Fw(P)1986 3573 y Fm(\000)p Fn(;\037;\015)2179 3561 y Fp(con)n(tains)e(a)h(free)g(algebra)f(with)0 3661 y(t)n(w)n(o)g(generators)e(\(in)j(this)g(case)f(task)g(\(2\))h (could)f(b)r(e)h(to)r(o)f(complicated\).)100 3760 y(A)n(tten)n(tion)33 b(in)g(this)g(article)g(is)f(concen)n(trated)g(at)h(studing)g(sets)g (\006)2231 3772 y Fm(\000)p Fn(;\037)2370 3760 y Fp(in)g(the)h(case)e (where)g(\000)h(is)0 3860 y(an)h(extended)g(Dynkin)h(graph.)56 b(Giv)n(en)34 b(result)f(here)h(is)g(full)h(description)f(of)g(the)h (set)f(\006)2877 3870 y Fm(~)2862 3885 y Fn(D)2916 3893 y Fi(4)2948 3885 y Fn(;\037)3014 3860 y Fp(,)i(the)0 3962 y(conditions)24 b(under)h(whic)n(h)f(sets)h(\006)1081 3974 y Fm(\000)p Fn(;\037)1212 3962 y Fp(are)f(in\014nite,)i(and)e(the) h(conditions)g(under)f(whic)n(h)h(there)f(exist)0 4062 y Fw(\003)p Fp(-represen)n(tations)h(of)j Fw(P)798 4074 y Fm(\000)p Fn(;\037;\015)990 4062 y Fp(on)g(sp)r(ecial)f(case)g(where) g Fo(\015)i Fp(=)23 b Fo(!)2004 4074 y Fm(\000)2076 4062 y Fp(\(see)28 b(section)g(1)f(for)g(the)i(di\014nition)0 4162 y(of)f Fo(!)147 4174 y Fm(\000)191 4162 y Fp(\).)1022 4331 y(1.)41 b Fq(Description)32 b(of)f(set)h Fp(\006)2029 4341 y Fm(~)2014 4356 y Fn(D)2068 4364 y Fi(4)2101 4356 y Fn(;\037)100 4488 y Fp(As)f(it)i(w)n(as)d(sho)n(wn)h(in)i([11)o(])f (the)g(set)g(\006)1352 4498 y Fm(~)1337 4513 y Fn(D)1391 4521 y Fi(4)1423 4513 y Fn(;\037)1520 4488 y Fp(can)g(b)r(e)g(reduced)f (to)h(the)g(structure)f(of)h(set)g(\006)3013 4500 y Fn(D)3067 4508 y Fi(4)3100 4500 y Fn(;\037)3165 4488 y Fp(.)0 4595 y(Complete)c(description)f(of)g(set)h(\006)1083 4607 y Fn(D)1137 4615 y Fi(4)1169 4607 y Fn(;\037)1262 4595 y Fp(w)n(as)f(giv)n(en)g(in)h([7)o(]:)455 4749 y(\006)515 4764 y Fn(D)569 4772 y Fi(4)602 4764 y Fn(;)p Fm(\()p Fn(\013)691 4772 y Fi(1)723 4764 y Fn(;\013)786 4772 y Fi(2)818 4764 y Fn(;\013)881 4772 y Fi(3)913 4764 y Fm(\))967 4749 y Fp(=)22 b Fw(f)p Fp(0)p Fo(;)14 b Fp(\()p Fo(\013)1260 4761 y Fm(1)1315 4749 y Fp(+)k Fo(\013)1451 4761 y Fm(2)1507 4749 y Fp(+)g Fo(\013)1643 4761 y Fm(3)1680 4749 y Fp(\))p Fo(=)p Fp(2)p Fw(g)g([)g(f)1971 4671 y Fh(X)1976 4849 y Fn(i)p Fj(2)p Fn(J)2105 4749 y Fo(\013)2158 4761 y Fn(i)2186 4749 y Fo(;)c(J)30 b Fw(\032)23 b(f)p Fp(1)p Fo(;)14 b Fp(2)p Fo(;)g Fp(3)p Fw(gg)p Fo(;)0 4962 y Fp(Let)25 b Fo(\013)199 4974 y Fn(i)227 4962 y Fo(;)14 b(i)23 b Fp(=)f(1)p Fo(;)14 b(:)g(:)g(:)f(;)h Fp(4)25 b(denote)g(i-th)g(comp)r(onen)n(t)g(of)g(the)g(c)n(haracter)e Fo(\037)i Fp(and)g Fo(\013)f Fp(=)e Fo(\013)2582 4974 y Fm(1)2633 4962 y Fp(+)13 b Fo(\013)2764 4974 y Fm(2)2815 4962 y Fp(+)g Fo(\013)2946 4974 y Fm(3)2997 4962 y Fp(+)g Fo(\013)3128 4974 y Fm(4)3165 4962 y Fp(.)0 5062 y(The)28 b(set)f(\006)375 5072 y Fm(~)360 5087 y Fn(D)414 5095 y Fi(4)447 5087 y Fn(;\037)540 5062 y Fp(satisfy)g(the)h(follo)n(wing)f (prop)r(erties)f(\(see)i([11)o(]\))141 5186 y(\(1\))42 b(\006)364 5196 y Fm(~)349 5211 y Fn(D)403 5219 y Fi(4)435 5212 y Fn(;\037)524 5186 y Fw(\032)22 b Fp([0)p Fo(;)14 b(\013)p Fp(];)141 5294 y(\(2\))42 b(\006)364 5304 y Fm(~)349 5319 y Fn(D)403 5327 y Fi(4)435 5319 y Fn(;\037)524 5294 y Fw(3)602 5231 y Fh(P)690 5318 y Fn(i)p Fj(2)p Fn(J)818 5294 y Fo(\013)871 5306 y Fn(i)899 5294 y Fo(;)14 b(J)31 b Fw(\032)23 b(f)p Fp(0)p Fo(;)14 b Fp(1)p Fo(;)g Fp(2)p Fo(;)g Fp(3)p Fo(;)g Fp(4)p Fw(g)p Fp(;)p eop end %%Page: 3 3 TeXDict begin 3 2 bop 0 50 a Fm(ON)29 b(EXISTENCE)f(OF)h Fj(\003)p Fm(-REPRESENT)-5 b(A)g(TIONS)28 b(OF)h(CER)-5 b(T)g(AIN)29 b(ALGEBRAS)g(RELA)-5 b(TED)29 b(TO)g(EXTENDED)g(D)n(YNKIN) g(GRAPHS)-33 b(3)141 249 y Fp(\(3\))42 b Fo(\034)32 b Fw(2)24 b Fp(\006)511 259 y Fm(~)496 274 y Fn(D)550 282 y Fi(4)583 274 y Fn(;\037)671 249 y Fw(\()-14 b(\))23 b Fo(\013)c Fw(\000)f Fo(\034)33 b Fw(2)23 b Fp(\006)1223 259 y Fm(~)1208 274 y Fn(D)1262 282 y Fi(4)1295 274 y Fn(;\037)1360 249 y Fp(;)0 370 y(Third)h(prop)r(ert)n(y)f(means)h(that) h(\006)1071 380 y Fm(~)1056 395 y Fn(D)1110 403 y Fi(4)1143 395 y Fn(;\037)1232 370 y Fp(is)f(symmetric)g(around)2002 337 y Fn(\013)p 2002 351 44 4 v 2007 399 a Fm(2)2055 370 y Fp(,)h(therefore)e(w)n(e)h(will)h(study)f(the)h(set)0 477 y(\006)75 487 y Fm(~)60 502 y Fn(D)114 510 y Fi(4)147 502 y Fn(;\037)230 477 y Fw(\\)19 b Fp([0)p Fo(;)416 444 y Fn(\013)p 416 458 V 421 506 a Fm(2)469 477 y Fp(\).)100 580 y(Notice)36 b(that)i(in)f(the)g(case)f(where)g(at)h(least)g(one)f (comp)r(onen)n(ts)g(of)h(the)g(c)n(haracter)e Fo(\037)2873 592 y Fn(i)2939 580 y Fd(>)j Fo(\013)g Fp(it)0 679 y(isn't)29 b(hard)g(to)g(sho)n(w)f(that)h(corresp)r(onding)f(pro)5 b(jection)28 b(equals)g(to)h(0)g(or)f Fo(I)36 b Fp(in)29 b(the)h(represen)n(tation,)0 779 y(hence)i(the)g(structure)g(of)g(set)f (\006)1050 789 y Fm(~)1035 804 y Fn(D)1089 812 y Fi(4)1122 804 y Fn(;\037)1219 779 y Fp(is)h(the)h(same)e(to)h(the)g(structure)f (of)h(\006)2439 791 y Fn(D)2493 799 y Fi(4)2526 791 y Fn(;\037)2591 779 y Fp(.)50 b(Therefore)31 b(it)h(is)0 881 y(in)n(teresting)23 b(to)g(study)g(the)h(case)e(where)h(all)g(comp) r(onen)n(ts)g(of)g(c)n(haracter)f Fo(\037)h Fp(are)f(less)h(than)2843 849 y Fn(\013)p 2843 863 V 2848 910 a Fm(2)2896 881 y Fp(.)35 b(In)24 b(this)0 981 y(case)i(the)h(set)f(\006)520 991 y Fm(~)505 1006 y Fn(D)559 1014 y Fi(4)592 1006 y Fn(;\037)684 981 y Fp(is)g(quite)h(di\013eren)n(t)g(from)f(\006)1557 993 y Fn(D)1611 1001 y Fi(4)1644 993 y Fn(;\037)1709 981 y Fp(,)h(furthermore)f(it)h(is)f(in\014nite.)38 b(The)26 b(follo)n(wing)0 1088 y(prop)r(ositions)h(giv)n(e)g(complete)h (description)f(of)h(the)h(set)f(\006)1861 1098 y Fm(~)1846 1113 y Fn(D)1900 1121 y Fi(4)1932 1113 y Fn(;\037)2026 1088 y Fp(\(exact)f(tec)n(hnique)h(and)g(pro)r(ofs)g(can)0 1195 y(b)r(e)g(found)g(in)g([11)o(]\))0 1346 y Fx(Lemma)40 b(1.)k Fc(The)38 b(set)d Fp(\006)853 1356 y Fm(~)838 1371 y Fn(D)892 1379 y Fi(4)925 1371 y Fn(;\037)1027 1346 y Fc(c)l(ontains)h(the)g(in\014nite)g(series)h Fp(\006)2100 1358 y Fj(1)2206 1346 y Fc(with)g(limit)g(p)l(oint)2823 1313 y Fn(\013)p 2823 1327 V 2828 1374 a Fm(2)2912 1346 y Fc(and)g(the)0 1448 y(\014nite)29 b(series)i Fp(\006)509 1460 y Fm(0)546 1448 y Fc(.)39 b(This)31 b(two)e(series)i(ar)l(e)f (describ)l(e)l(d)h(by)f(the)g(fol)t(lowing)j(rule:)141 1566 y Fp(\(1\))42 b Fc(when)30 b Fo(\013)554 1578 y Fm(2)610 1566 y Fp(+)18 b Fo(\013)746 1578 y Fm(3)806 1566 y Fo(>)23 b(\013)947 1578 y Fm(1)1003 1566 y Fp(+)18 b Fo(\013)1139 1578 y Fm(4)1206 1566 y Fc(then)29 b Fp(\006)1450 1578 y Fj(1)1544 1566 y Fp(=)1631 1499 y Fh(\010)1690 1534 y Fn(\013)p 1690 1548 V 1695 1595 a Fm(2)1761 1566 y Fw(\000)1854 1532 y Fn(\013)1897 1540 y Fi(1)p 1854 1547 76 4 v 1855 1595 a Fm(2)p Fn(n)1940 1566 y Fw(j)p Fo(n)23 b Fw(2)g Fk(N)2174 1499 y Fh(\011)2252 1566 y Fc(and)289 1699 y Fp(\006)349 1711 y Fm(0)409 1699 y Fp(=)497 1607 y Fh(n)562 1666 y Fn(\013)p 562 1680 44 4 v 567 1728 a Fm(2)634 1699 y Fw(\000)747 1665 y Fn(\013)p Fj(\000)p Fm(2)p Fn(\013)918 1673 y Fi(4)p 727 1680 245 4 v 727 1728 a Fm(2\(2)p Fn(n)p Fj(\000)p Fm(1\))981 1699 y Fw(j)p Fo(n)g(<)1365 1665 y Fn(\013)1408 1673 y Fi(1)p 1174 1680 457 4 v 1174 1728 a Fn(\013)1217 1736 y Fi(2)1250 1728 y Fm(+)p Fn(\013)1344 1736 y Fi(3)1376 1728 y Fj(\000)p Fn(\013)1471 1736 y Fi(1)1504 1728 y Fj(\000)p Fn(\013)1599 1736 y Fi(4)1641 1699 y Fo(;)14 b(n)23 b Fw(2)g Fk(N)1889 1607 y Fh(o)141 1857 y Fp(\(2\))42 b Fc(when)30 b Fo(\013)554 1869 y Fm(2)610 1857 y Fp(+)18 b Fo(\013)746 1869 y Fm(3)806 1857 y Fo(<)23 b(\013)947 1869 y Fm(1)1003 1857 y Fp(+)18 b Fo(\013)1139 1869 y Fm(4)1206 1857 y Fc(then)29 b Fp(\006)1450 1869 y Fj(1)1544 1857 y Fp(=)1631 1765 y Fh(n)1697 1824 y Fn(\013)p 1697 1838 44 4 v 1702 1886 a Fm(2)1768 1857 y Fw(\000)1881 1823 y Fn(\013)p Fj(\000)p Fm(2)p Fn(\013)2052 1831 y Fi(4)p 1861 1838 245 4 v 1861 1886 a Fm(2\(2)p Fn(n)p Fj(\000)p Fm(1\))2115 1857 y Fw(j)p Fo(n)23 b Fw(2)h Fk(N)2350 1765 y Fh(o)2435 1857 y Fc(and)289 2015 y Fp(\006)349 2027 y Fm(0)409 2015 y Fp(=)497 1922 y Fh(n)562 1982 y Fn(\013)p 562 1996 44 4 v 567 2043 a Fm(2)634 2015 y Fw(\000)727 1981 y Fn(\013)770 1989 y Fi(1)p 727 1996 76 4 v 728 2043 a Fm(2)p Fn(n)812 2015 y Fw(j)p Fo(n)f(<)1196 1981 y Fn(\013)1239 1989 y Fi(1)p 1006 1996 457 4 v 1006 2043 a Fn(\013)1049 2051 y Fi(1)1081 2043 y Fm(+)p Fn(\013)1175 2051 y Fi(4)1208 2043 y Fj(\000)p Fn(\013)1303 2051 y Fi(2)1335 2043 y Fj(\000)p Fn(\013)1430 2051 y Fi(3)1473 2015 y Fo(;)14 b(n)22 b Fw(2)i Fk(N)1721 1922 y Fh(o)141 2147 y Fp(\(3\))42 b Fc(when)30 b Fo(\013)554 2159 y Fm(2)610 2147 y Fp(+)18 b Fo(\013)746 2159 y Fm(3)806 2147 y Fp(=)23 b Fo(\013)947 2159 y Fm(1)1003 2147 y Fp(+)18 b Fo(\013)1139 2159 y Fm(4)1206 2147 y Fc(then)29 b Fp(\006)1450 2159 y Fj(1)1544 2147 y Fp(=)1631 2080 y Fh(\010)1690 2115 y Fn(\013)p 1690 2129 44 4 v 1695 2176 a Fm(2)1761 2147 y Fw(\000)1854 2113 y Fn(\013)1897 2121 y Fi(1)p 1854 2128 76 4 v 1871 2176 a Fn(n)1940 2147 y Fw(j)p Fo(n)23 b Fw(2)g Fk(N)2174 2080 y Fh(\011)2252 2147 y Fc(and)30 b Fp(\006)2473 2159 y Fm(0)2534 2147 y Fp(=)22 b Fk(?)p Fc(.)0 2298 y Fx(Theorem)31 b(1.)142 2435 y Fp(\006)217 2445 y Fm(~)202 2460 y Fn(D)256 2468 y Fi(4)289 2460 y Fn(;\037)372 2435 y Fw(\\)19 b Fp([0;)14 b Fo(\013=)p Fp(2\))22 b(=)h(\006)887 2447 y Fj(1)976 2435 y Fw([)c Fp(\006)1110 2447 y Fm(0)1165 2435 y Fw([)g Fp(\006)1299 2447 y Fm(1)1355 2435 y Fw([)f Fp(\006)1488 2401 y Fn(i)1488 2455 y Fm(2)1544 2435 y Fw([)h Fp(\006)1678 2447 y Fm(3)1734 2435 y Fw([)f Fp(\006)1867 2447 y Fm(4)1923 2435 y Fw([)h Fp(\006)2057 2395 y Fn(j)2057 2457 y Fm(5)2094 2435 y Fo(;)99 b(i)22 b Fp(=)h(2)p Fo(;)14 b Fp(3)p Fo(;)g Fp(4)p Fo(;)97 b(j)28 b Fp(=)23 b(1)p Fo(;)14 b Fp(2)p Fo(;)g Fp(3)p Fo(;)0 2574 y Fc(wher)l(e)0 2740 y Fp(\006)60 2752 y Fm(1)120 2740 y Fp(=)208 2623 y Fh(\032)280 2684 y Fo(\013)p 280 2721 54 4 v 286 2797 a Fp(2)362 2740 y Fw(\000)598 2684 y Fo(\013)p 455 2721 341 4 v 455 2797 a Fp(2\(4)p Fo(n)k Fw(\000)g Fp(1\))805 2740 y Fw(j)34 b Fo(n)23 b(<)1131 2684 y(\013)1184 2696 y Fm(4)p 1033 2721 287 4 v 1033 2797 a Fp(4)p Fo(\013)1128 2809 y Fm(4)1183 2797 y Fw(\000)18 b Fo(\013)1329 2740 y(;)c(n)23 b(<)1557 2684 y(\013)c Fw(\000)f Fo(\013)1765 2696 y Fm(1)p 1537 2721 V 1537 2797 a Fo(\013)h Fw(\000)f Fp(4)p Fo(\013)1787 2809 y Fm(1)1833 2740 y Fo(;)c(n)23 b Fw(2)h Fk(N)2082 2623 y Fh(\033)2158 2740 y Fo(;)0 2972 y Fp(\006)60 2938 y Fn(i)60 2993 y Fm(2)120 2972 y Fp(=)208 2880 y Fh(n)273 2916 y Fo(\013)p 273 2953 54 4 v 279 3029 a Fp(2)355 2972 y Fw(\000)453 2916 y Fo(\013)506 2928 y Fn(i)p 448 2953 92 4 v 448 3029 a Fp(2)p Fo(n)549 2972 y Fw(j)g Fo(n)f(<)982 2916 y(\013)1035 2928 y Fn(i)p 767 2953 511 4 v 767 3029 a Fp(2)p Fo(\013)862 3041 y Fn(i)907 3029 y Fp(+)18 b(2)p Fo(\013)1085 3041 y Fm(4)1141 3029 y Fw(\000)g Fo(\013)1287 2972 y(;)c(n)23 b(<)1590 2916 y(\013)1643 2928 y Fn(i)p 1495 2953 273 4 v 1495 3029 a Fo(\013)1548 3041 y Fn(i)1594 3029 y Fw(\000)18 b Fo(\013)1730 3041 y Fm(1)1801 2972 y Fo(n)23 b(<)2070 2916 y(\013)2123 2928 y Fn(i)p 1971 2953 278 4 v 1971 3029 a Fp(4)p 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b(S.A.)c(Krugly)n(ak,)j(V.I.)d(Rabano)n(vic)n(h,)k(Y)-6 b(u.S.)31 b(Samoilenk)n(o)h Fg(On)h(sums)h(of)f(pr)l(oje)l(ctions)p Fv(,)h(F)-6 b(unc.)33 b(analis)e(and)h(its)125 5131 y(application.)25 b(\(2002\).36)g(,)f(1.)f(pp.20-35.)35 5214 y(4.)35 b(M.)21 b(A.)g(Vlasenk)n(o,)h(A.)f(S.)g(Mellit,)g(and)h(Y)-6 b(u.)21 b(S.)h(Samoilenk)n(o,)g Fg(On)h(algebr)l(as)i(gener)l(ate)l(d)f (with)g(line)l(arly)g(dep)l(endent)125 5297 y(gener)l(ators)j(that)e (have)h(given)f(sp)l(e)l(ctr)l(a)p Fv(,)g(F)-6 b(unct.)24 b(Anal.)f(Appl.)g(3)1825 5342 y(\026)1861 5297 y(9)g(\(2005\),)j(no.)d (3,)h(pp.14-27.)p eop end %%Page: 9 9 TeXDict begin 9 8 bop 0 50 a Fm(ON)29 b(EXISTENCE)f(OF)h Fj(\003)p Fm(-REPRESENT)-5 b(A)g(TIONS)28 b(OF)h(CER)-5 b(T)g(AIN)29 b(ALGEBRAS)g(RELA)-5 b(TED)29 b(TO)g(EXTENDED)g(D)n(YNKIN) g(GRAPHS)-33 b(9)35 249 y Fv(5.)35 b(An)n(ton)g(Mellit,)g Fg(Certain)f(Examples)i(of)f(Deforme)l(d)h(Pr)l(epr)l(oje)l(ctive)f(A)n (lgebr)l(as)h(and)f(Ge)l(ometry)g(of)g(Their)g(*-)125 332 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