Symmetry in Nonlinear Mathematical Physics - 2009


Vasyl Fedorchuk (Pedagogical University, Krakow, Poland & Pidstryhach Institute of Applied Problems of Mechanics and Mathematics, Lviv, Ukraine)
Volodymyr Fedorchuk (Pidstryhach Institute of Applied Problems of Mechanics and Mathematics, Lviv, Ukraine)

On invariant operators of the four-dimensional non-conjugate subalgebras of the Lie algebra of the Poincaré group P(1,4)

Abstract:
By using the Mubarakzyanov's classification [1] of the low-dimensional real Lie algebras and the results obtained in [2], we have constructed invariant operators (generalized Casimir operators) for all four-dimensional non-conjugate subalgebras of the Lie algebra of the Poincaré group P(1,4).

1. Mubarakzyanov G.M., On solvable Lie algebras, Izv. Vys. Ucheb. Zaved. Mat., 1963, no 1 (32), 114-123.
2. Patera J., Sharp R.T., Winternitz P., Zassenhaus H., Invariants of real low dimension Lie algebras, J. Math. Phys., 1976, 17, no 6, 986-994.