Vasyl Fedorchuk (Pedagogical Academy, Institute of Mathematics, Kraków, Poland and Pidstryhach
Institute of Applied Problems of Mechanics and Mathematics of NAS of Ukraine, Lviv, Ukraine)
Classification of the low-dimensional non-conjugate subalgebras of the Lie
algebra of the Poincaré group P(1,4)
Abstract:
The complete classification of all non-conjugate subalgebras of dimensions £ 3
of the Lie algebra of the Poincaré group P(1,4) is performed [ 1 ].
By now, using the Mubarakzyanov's classification [ 2, 3 ] of the low-dimensional real
Lie algebras and results obtained in [ 4 ], we have classified almost all four-dimensional
and almost all five-dimensional non-conjugate subalgebras of the Lie algebra
of the Poincaré group P(1,4) into isomorphism classes.
- Fedorchuk V.M., Fedorchuk V.I. On classification of the low-dimensional non-conjugate subalgebras
of the Lie algebra of the Poincaré group P(1,4), Proceedings of Institute of Mathematics of NAS
of Ukraine, 2006, V.3, N 2, 302-308.
- Mubarakzyanov G.M., On solvable Lie algebras, Izv. Vys. Ucheb.
Zaved. Mat., 1963, N 1(32), 114-123.
- Mubarakzyanov G.M., The classification of the real structures of
five-dimensional Lie algebras, Izv. Vys. Ucheb. Zaved. Mat., 1963, N
3(34), 99-106.
- Patera J., Sharp R.T., Winternitz P., Zassenhaus H. Invariants of
real low dimension Lie algebras, J. Math. Phys., 1976, 17, N6, 986-994.
Joint work with Volodymyr Fedorchuk (Pidstryhach
Institute of Applied Problems of Mechanics and Mathematics of NAS of Ukraine, Lviv, Ukraine).