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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 560178, 16 pages
http://dx.doi.org/10.1155/2013/560178
Research Article

Invariant Operators of Five-Dimensional Nonconjugate Subalgebras of the Lie Algebra of the Poincaré Group P(1,4)

1Institute of Mathematics, Pedagogical University, 2 Podchorążych Street, 30-084 Cracow, Poland
2Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, 3b Naukova Street, Lviv 79601, Ukraine

Received 1 July 2013; Revised 17 September 2013; Accepted 19 September 2013

Academic Editor: Emrullah Yaşar

Copyright © 2013 Vasyl Fedorchuk and Volodymyr Fedorchuk. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We have classified all five-dimensional nonconjugate subalgebras of the Lie algebra of the Poincaré group P(1,4) into classes of isomorphic subalgebras. Using this classification, we have constructed invariant operators (generalized Casimir operators) for all five-dimensional nonconjugate subalgebras of the Lie algebra of the Poincaré group P(1,4) and presented them in the explicit form.