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

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.Abstract and Applied Analysis the Lie algebra of the Poincaré group P(1,4) into isomorphism classes as well as their invariant operators. The conclusions and results are discussed in Section 6.

On Classification of Symmetry Reductions for the Eikonal Equation

“…Taking into account the complete classification of real structures of Lie algebras of a dimension less or equal four obtained by Mubarakzyanov in [41], we classify all the three-dimensional nonconjugate subalgebras of the Lie algebra of the group P(1, 4) into classes of isomorphic subalgebras (see, [42]). …”

On Symmetry Reduction of the (1 + 3)-Dimensional Inhomogeneous Monge-Ampère Equation to the First-Order ODEs

“…It is known [40] that the Lie algebra of the group P (1, 4) contains three-dimensional nonconjugate subalgebras of the following types: 1 , A 3,1 , A 3,2 , A 3,3 , A 3,4 , A 3,6 , A a 3,7 , A 3,8 , A 3,9 . From the results obtained it follows that -the reductions to the first-order linear ODEs can be obtained using some subalgebras of the following types: 3A 1 , A 3,6 .…”

“…In order to perform symmetry reduction as well as to construct classes of independent invariant solutions for the equation under consideration, we used the structural properties of three-dimensional nonconjugate subalgebras of the Lie algebra of the group P (1, 4) [40].…”

“…The classification of all nonconjugate subalgebras of the Lie algebra of the group P (1, 4) of dimensions ≤ 3 was performed in [40].…”