# Yuriy Drozd - Publications

Books:

1. (with V. V. Kirichenko) Higher Algebra. Kiev University, p.I, 1971, p.II, 1973.
2. (with V. V. Kirichenko) Finite Dimensional Algebras. Vyshcha Shkola, Kiev, 1980 Download DJVU (Russian) (English enlarged edition: Springer-Verlag, 1994.)
5. Introduction to Algebraic Geometry. Klasyka Publishers, L'viv, 2004.
7. Vector Bundles over Projective Curves. IMPA, Rio de Janeiro, 2008. (Ukrainian revised version: Inst. Math. NAS Ukraine, Kyiv, 2010).
8. (with I.Burban) Maximal Cohen-Macaulay Modules over Non-Isolated Surface Singularities. Memoirs AMS, v.248, No.1178, 2017.

Research Articles:

1. (with I.Burban) Non-commutative nodal curves and derived tame algebras. arXiv:1805.05174 [math.AG]
2. (with I.Burban and V.Gavran) Minors and resolutions of non-commutative schemes. Eur. J. Math, 3:2 (2017) 311-341. (arXiv:1501.06023 [math.AG])
3. (with A.I.Plakosh) Cohomologies of finite abelian groups. Algebra Discrete Math. 24:1 (2017) 144-157. (arXiv:1709.05616 [math.Gr])
4. (with I.Burban and V.Gavran) Minors and categorical resolutions. Singularities and Computer Algebra. Springer, 2017, 71-95.
5. (with N.Golovashchuk and V.Zembyk) Representations of nodal algebras of type E. Algebra Discrete Math. 23:1 (2017) 16-34.
6. Arch. Math. 108 (2017) 569-579 (arXiv:1610.05033 [math.AC])
7. (with A.Plakosh) On nilpotent Chernikov 2-groups with elementary tops, Algebra Discrete Math.  22:2 (2016), 201-208 (arXiv:1610.05030 [math.GR])
8. (with I.Burban and V.Gavran) Singular curves and quasi-hereditary algebras. Intern. Math. Research Notices 2017(3), 895-920 (2017) (arXiv:1503.04565 [math.AG])
9. (with A.Plakosh) On nilpotent Chernikov p-groups with elementary tops. Arch. Math. 103 (2014) 401-409. ( arXiv:1409.7188 [math.GR]).
10. (with V.Zembyk) Representation type of nodal algebras of type D. Ukr. Math. J. 66, No.7 (2014) 930-938.
11. (with P.Kolesnyk) Atoms in the p-localizations of stable homotopy category. Ukr. Math. J. 66, No.4 (2014) 458-472. (arXiv:1305.2589 [math.AT])
12. (with I.Burban and V.Gavran) Non-commutative schemes and categorical resolutions. Preprint 2014-6. Max-Plank-Institut für Mathematik, 2014.
13. (with O.Tovpyha) Graded Cohen-Macaulay rings of wild Cohen-Macaulay type. J. Pure Appl. Algebra, 218, no.9 (2014) 1628-1634. (arXiv:1212.6557 [math.AG]).
14. (with V.Gavran) On Cohen-Macaulay modules over non-commutative surface singularities. Cent. Eur. J. Math. 12, no.5 (2014) 675-687. (arXiv:1301.2999 [math.AG]).
15. (with V.Zembyk) Representations of nodal algebras of type A. Algebra Discrete Math. 15, No.2 (2013), 179-200.
16.  (with V.Bekkert and V.Futorny) Tilting, deformations and representations of linear groups over Euclidean algebras. J. Pure Appl. Algebra, 217, no.6 (2013), 1141-1152. (arXiv:0810.2037 [math.RT])
17.  (with D.Voloshyn) Derived categories of nodal curves. (Ukrainian) Ukr. Math. J. 64, No.7 (2012), 1033-1040. (English translation: Ukr.Math.J. (Springer) 64 (2013), 1077-1184).
18. (with R.Skuratovskii) One branch curve singularities with at most 2-parameter families of ideals. Algebra and Discrete Math. 13, no.2 (2012), 209-219. ( arXiv 1201.6579 [math.AC]). Download PDF
19. (with P.Kolesnyk) On genera of polyhedra. Central European J. Math. 10 (2012), 401-410. (arXiv:1104.5526 [math.AT]). Download PDF
20.  (with L.Bodnarchuk and G.-M.Greuel) Simple vector bundles on plane degenerations of an elliptic curve. Trans. Amer. Math. Soc.364 (2012), 137-174. ( arXiv:0903.4966 [math.AG]). Download PDF
21. (with D.Voloshyn) Vector bundles over noncommutative nodal curves. Ukr. Math. J. 64, No.2 (2012), 185-199. (arXiv:1201.1710 [math.AG]). Download PDF
22. (with I.Burban) Tilting on non-commutative rational projective curves. Math. Ann. 351 (2011), 665-709. (arXiv:0905.1231 [math.AG])
23.  (with I.Burban) Maximal Cohen-Macaulay modules over non-isolated surface singularities. arXiv:1002.3042 [math.AG]. Download PDF
24. (with R.Skuratovskii) Cubic rings and their ideals. Ukr. Math. J. 62,  No. 4 (2010), 530-536.   (arXiv:1001.0230 [math.AG])
25. Matrix problems, triangulated categories and stable homotopy types. São Paulo Journal of Mathematical Sciences 4 (2010), 209-249. (arXiv:0903.5185 [math.AT])
26. (with L.Bodnarchuk) One class of wild but brick-tame matrix problems. J.Algebra 323 (2010), 3004-3019.  ( arXiv:0903.4374 [math.RT])
27. (with V.Bekkert) Derived categories for algebras with radical square zero. Algebras, Representations and Applications. Contemp. Math. 483 (2009), 55-62. ( arXiv:0812.4818 [math.RT])
28. (with V.Bekkert and V.Futorny) Derived tame local and two-point algebras. J. Algebra 302 (2009), 2433-2448. (arXiv:0812.4783 [math.RT]) Download PDF
29.  (with R.Skuratovskii) Generators and relations for wreath products. Ukrainian Math. J. 90 (2008), 997-999. (arXiv:0810.0769 [math.GR]) Download PDF
30. (with I.Burban) Maximal Cohen-Macaulay modules over surface singularities. Trends in Representations of Algebras and Related Topics. EMS Publishing House, 2008, 101--166. (arXiv:0803.0117 [math.AG]) Download PDF
31. Group action on bimodule categories. Algebra and Discrete Math. no. 3 (2008), 50-68. (arXiv:0802.4266 [math.RT]) Download PDF
32. (with P.Kolesnik) Automorphisms of incidence algebras. Comm. Alg. 35 (2007). Download PDF
33. (with V.Mazorchuk) Koszul duality for extension algebras of standard modules. J. Pure Appl. Algebra. 211 (2007), 484-496. Download PDF
34. (with R.Bautista, Xiyangyong Zeng and Yingbo Zhang) On Hom-spaces of tame algebras. Central European J. Math. 5 (2007), 215-263. Download PDF
35. Derived categories of modules and coherent sheaves in: Singularities and computer algebra. London Mathematical Society Lecture Note Series 324 (2006), 79-128. Download PDF
36. (with L.Bodnarchuk, I.Burban and G.-M.Greuel) Vector bundles and torsion free sheaves on degenerations of elliptic curves. in: Global Aspects of Complex Geometry. Springer, 2006, 83-128. Download PDF
37. (with V.M.Mazorchuk) Representation type of ${}^\infty_\lambda\mathcal H_\mu^1$. Quaterly J. Math. 57 (2006), 319--338 (arXiv:math.RT/0412301). Download PDF
38. (with P.Kolomiets) Intersection of irreducible components of biSchubert manifolds. Zbirnyk prats’ Inst.Mat. NASU 3, №3 (2006) 180—200.
39. (with I.Burban) Derived categories for nodal rings and projective configurations. in: Noncommutative Algebra and Geometry. Lecture Notes in Pure and Applied Mathematics 243 (2005), 23-46. Download PDF
40. On classification of torsion free polyhedra. Preprint MPI 2005-99, Max-Plank-Institut für Mathematik, 2005. Download PDF \
41. Semi-continuity for derived categories. Algebras and Representation Theory 8 (2005), 239--248 (arXiv:math.RT/0212015). Download PDF
42. (with P.S.Kolomiets) On some generalization of Schubert's varieties. in: Computational commutative and non-commutative algebraic geometry. NATO Science Series III: Computer & Systems Sciences 196 (2005), 79-89.
43. (with I.Burban) On derived categories of certain associative algebras in: Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry. Field Institute Communications 45. AMS, 2004, 109--128. Download PDF
44. (with V.M.Mazorchuk) Koszul duality for extension algebras of standard modules. Preprint 2004-48, Uppsala University, 2004 (arXiv:math.RT/0411528). Download PDF
45. (with E.A.Kubichka) Dimensions of finite type for representations of partially ordered sets. Algebra and Discrete Math. 3, No.3 (2004), 20-36 (arXiv:math.RT/0404242). Download PDF
46. Matrix problems and stable homotopy types of polyhedra. Central European J. Math. 2 (2004), 420--447 (arXiv:math.AT/0404252). Download PDF
47. (with V.I.Bekkert) Tame-wild dichotomy for derived categories. arXiv:math.RT/0310352 (submitted to J. London Math. Soc.) Download PDF
48. Derived tame and derived wild algebras. Algebra and Discrete Math. 3, No.1 (2004), 57-74 (arXiv:math.RT/0310171). Download PDF
49. Vector bundles and Cohen-Macaulay modules. Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry. Field Institute Communications 40. AMS, 2004, 189--222. (arXiv:math.AG/0310368) Download PDF
50. (with L.Bodnarchuk) Stable vector bundles over cuspidal cubics. Central Eurpean J.Math. 1 (2003) 650-660. Download PDF
51. (with I.Burban) Derived categories of nodal algebras. J. Algebra 272 (2004) 46--94. Download PDF
52. (with G.-M. Greuel and I. Kashuba) On Cohen-Macaulay modules on surface singularities. Moscow Math. J. 3 (2003), 397-418. Download PDF
53. On polynomial functors. Visnyk Lviv Univ., 61 (2003) 67-77. Download PDF
54. (with I.Burban) Coherent sheaves on rational curves with simple double points and transversal intersections. Duke Math. J. 121 (2004) 189-229. Download PDF
55. On cubic functors. Communications in Algebra, 173 (2003) 1147-1173. Download PDF
56. (with I.Burban) Derived categories and matrix problems. In: Algebraic structures and their Applications. Ukrainian Mathematical Congress Proceedings. Institute of Mathematics, Kyiv, 2002, 201-211.
58. (with G.-M. Greuel) Tame and wild projective curves and classification of vector bundles. J. Algebra, 246 (2001) 1-54. Download PDF
59. (with H.-J. Baues) Classification of stable homotopy types with torsion-free homology. Topology 40 (2001) 789-821. Download PDF
60. (with I. Burban and G.-M. Greuel) Vector bundles on singular projective curves, in: Applications of Algebraic Geometry to Coding Theory, Physics and Computation. Kluwer Academic Publishers, 2001, 1-15.
62. (with I.Burban) On derived categories of vector bundles and some associative algebras, Preprint, University of Kaiserslautern, 2001.
63. (with H.-J. Baues) Indecomposable homotopy types with at most two non-trivial homology groups. In: Groups of Homotopy Self-Equivalences and Related Topics. Contemporary Mathematics, 274 (2001) 39-56. Download PDF
64. Cohen-Macaulay modules and vector bundles. In: Interaction between Ring Theory and Representations of Algebras, Marcel Decker, New York, 2000, 107-130.
65. (with H.-J. Baues) Representation theory of homotopy types with at most two non-trivial homotopy groups, Math. Proc. Cambridge Phil. Soc. 128 (2000), 283-300. Download PDF
66. (with S. Ovsienko) Coverings of tame boxes and algebras, Preprint MPI 00-26, Max-Plank-Institut für Mathematik, Bonn, 2000 (submitted to Proceedings of the London Mathematical Society). Download PDF
67. (with H.-J. Baues) The homotopy classification of (n-1)-connected (n+4)-dimensional polyhedra with torsion free homology, Expo. Math. 17 (1999), 161-179.Download PDF
68. (with V. V. Kirichenko and S. A. Ovsienko) On systems of orthogonal permutations, Matem. Studii 2, no.1 (1999) 3-6.
69. (with G.-M. Greuel) On Schappert's characterization of strictly unimodal plane curve singularities, in: Singularities: The Brieskorn Anniversary Volume, Birkhäuser, 1998, 3-26. Download PDF
70. Module-theoretical propertiers of "good" curve singularities, in: Rings, Hopf Algebras and Brauer Groups, Marcel Decker, New York, 1998, 111-117. Download PDF
71. Representations of bisected posets and reflection functors, In: Algebras and Modules. II, CMS Conference Proceedings, vol. 24, Amer. Math. Soc., 1998, 153-165.Download PDF
72. (with K. W. Roggenkamp) On the global structure of regular orders of dimension two, Commun. Algebra, 25 (1997), 1-9.
73. (with G.-M. Greuel) Semi-continuity for Cohen-Macaulay modules, Math. Ann., 306 (1996) 371-389.Download PDF
74. (with B. L. Guzner, S. A. Ovsienko) Weight modules over generalized Weyl algebras, J. Algebra, 184 (1996) 491-504.
75. Cohen-Macaulay modules over Cohen-Macaulay algebras. In: Representation Theory of Algebras and Related Topics, CMS Conference Proceedings, vol. 19, Amer. Math. Soc., 1996, p. 25-53. Download PDF
76. Quadratic forms in the old Kiev school. In: Quadratic Forms in the Representation Theory of Finite-Dimensional Algebras, Bielefeld, SFB 343, 1996, 2-1 - 2-12.
77. (with P. Dräxler, N. S. Golovashchuk, S. A. Ovsienko, M. V. Zeldich) Towards the classification of sincere weakly positive unit forms, European J. on Combinatorics, 16 (1995) 1-16.
78. (with K. W. Roggenkamp) Cohen-Macaulay rings of global dimension two and Krull dimension two, Comm. in Algebra, 22 (1994) 3297-3330.
79. (with V. Shapiro) Tame and wild two by two matrix orders, J. Algebra, 163 (1994) 258-264.
80. (with V. M. Futorny, S. A. Ovsienko) Harish-Chandra subalgebras and Gelfand-Zetlin modules. In: Finite Dimensional Algebras and Related Topics, Kluwer Acad. Publ., 1994, 79-95.
81. (with Gh. A. Noumi) Maximal orders in Lie algebra SL(2), Preprint 93-077, SFB 343, Univ. Bielefeld, 1993.
82. (with G.-M. Greuel) Cohen-Macaulay module type, Compositio Math., 89 (1993) 315-338.Download PDF
83. (with L. V. Izyumchenko) Representations of O-species, Ukrainian Math. J., 44 (1992) 572-574.
84. (with G.-M. Greuel) Tame-wild dichotomy for Cohen-Macaulay modules, Math. Ann., 294 (1992) 387-394.
85. (with V. M. Futorny, S. A. Ovsienko) Gelfand-Zetlin modules over Lie algebra SL(3), Contemp. Math., 131, p.2 (1992) 23-30.
86. Representations of bocses and algebras, Contemp. Math. 131, p.2 (1992) 301-316.
87. Matrix problems, small reduction and representations of a class of mixed Lie groups, In: Representations of Algebras and Related Topics, Cambridge Univ. Press, 1992, 225-249.
88. (with S. A. Ovsienko, V. M. Futorny) On Gelfand-Zetlin modules, Suppl. Rend. Circ. Mat. Palermo, 26 (1991) 143-147.Download DjVu
89. (with S. A. Ovsienko, V. M. Futorny) S-homomorphism of Harish-Chandra and G-modules generated by semiprimitive element, Ukrainian Math. J., 42 (1990) 1031-1037.
90. (with L. F. Chernova) On lattices over Noetherian algebras, Ukrainian Math. J., 42 (1990) 604-610.
91. (with A. S. Timoshin) Representations of net subgroups and some of their generalizations, Preprint, Kiev, 1990.
92. Finite modules over pure Noetherian algebras, Trudy Mat. Inst. Steklov Acad. Sci. USSR, 183 (1990) 56-68. (English translation: Proc. Steklov Inst. of Math., 183 (1991) 97-108) Download PDF
93. (with V. M. Futorny, S. O. Ovsienko) Irreducible weight SL(3)-modules, Funk. Anal. Prilozh., 23(3) (1989) 57-58. Download PDF
94. (with V. Chepulich) One property of an order in the free semigroup. In: Algebraic Structures and Their Applications, Kiev, 1988, 167-169.
95. (with B. Yu. Furchin, S. O. Ovsienko) Categorical constructions in representation theory, In: Algebraic Structures and Their Applications, Kiev, 1988, 17-43.
96. (with L. F. Chernova) On lattices over pseudo-Bassian commutative rings, Mat. Zametki, 41 (1987) 475-478. Download PDF
97. (with L. Kaluzhnin, S. Zavalo) Development of algebraic research at Kiev University, Visnyk Kiev Univ., 27 (1985) 52-62.
98. On existence of maximal orders, Mat. Zametki, 37 (1985) 313-315.Download PDF
99. Four squares theorem, In: Mathematics Today, Kiev, 1983, 42-49.
100. On representations of Lie algebra SL(2), Visnyk Kiev Univ., 25 (1983) 70-77.
101. Complex numbers as similitudes of plane, In the World of Math., Kiev, 12 (1981) 27-36.
102. Modules over hereditary orders, Mat. Zametki, 29 (1981) 813-816. Download PDF
104. Tame and wild matrix problems, In: Representations and quadratic forms, Kiev, 1979, 39-74 (English translation in AMS Translations v.128).
105. (with V. M. Turchin) On locally conjugate orders, Mat. Zametki, 24 (1978) 871-878.Download PDF
106. On divisor semigroup of commutative ring, Trudy (Proc.) Steklov Math. Inst. Acad. Sci. USSR, 148 (1978) 156-167. Download PDF
107. (with V. M. Bondarenko) Representation type of finite groups, Zapiski Nauchn. Semin. LOMI, 71 (1977) 24-41. Download PDF
108. On tame and wild matrix problems, In: Matrix Problems, Kiev, 1977, 104-114.
110. Minkowski lemma and Pell equations, In the World of Math., Kiev, 7 (1976) 32-40.
111. On generalized uniserial rings, Mat. Zametki, 18 (1975) 705-710. Download PDF
112. Pythagorean triangles and quadratic curves, In the World of Math., Kiev, 6 (1975) 26-36.
113. (with N. M. Gubareni, V. V. Kirichenko) Right serial rings, Preprint, Kiev, 1975.
115. Coxeter transformations and representations of partially ordered sets, Funk. Anal. Prilozh., 8(3) (1974) 34-42. Download PDF
116. A generalization of a theorem of Dade, Dopovidi Acad. Sci. Ukraine, 3 (1974) 204-207.
117. (with V. V. Kirichenko, K. W. Roggenkamp) Orders with one irreducible representation, Dopovidi Acad. Sci. Ukraine, 1 (1974) 22-24.
118. (with V. V. Kirichenko) Primary orders with a finite number of indecomposable representations, Izvestia Acad. Sci. USSR, 37 (1973) 715-736. Download PDF
119. Minors and theorems of reduction, Coll. Math. Soc. J.Bolyai, 6 (1973) 173-176.
120. Indecomposable matrix rings of order two with a finite number of representations are Bassian, Mat. Zametki, 12 (1972) 601-604.
121. Matrix problems and categories of matrices, Zapiski Nauchn. Semin. LOMI, 28 (1972) 144-153. Download PDF
122. Representations of commutative algebras, Funk. Anal. Prilozh., 6(4) (1972) 41-43. Download PDF
123. (with V. V. Kirichenko) On quasi-Bassian orders, Izvestia Acad. Sci. USSR, 36 (1972) 328-370. Download PDF
124. Structure of genera of representations of non-semisimple rings, Mat. Zametki, 10(1971)63-67. Download PDF