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.
  1. 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.
  2. Mubarakzyanov G.M., On solvable Lie algebras, Izv. Vys. Ucheb. Zaved. Mat., 1963, N 1(32), 114-123.
  3. 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.
  4. 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).