Maximal Abelian Subalgebras of e(p,q) algebras

Details Maximal Abelian Subalgebras of e(p,q) algebras Maximal Abelian Subalgebras of e(p,q) algebras

1998-05-06

arxiv.org/abs/math/9805024v1

Lin. Algebra Appl., 291:245-274, 1999

Mathematics

Group Theory

29 pages, Latex

Scientific paper

Maximal abelian subalgebras of one of the classical real inhomogeneous Lie algebras are constructed, namely those of the pseudoeuclidean Lie algebra e(p,q). Use is made of the semidirect sum structure of e(p,q) with the translations T(p+q) as an abelian ideal. We first construct splitting MASAs that are themselves direct sums of abelian subalgebras of o(p,q) and of subalgebras of T(p+q). The splitting subalgebras are used to construct the complementary nonsplitting ones. We present general decomposition theorems and construct indecomposable MASAs for all algebras e(p,q), p \geq q \geq 0. The case of q=0 and 1 were treated earlier in a physical context. The case q=2 is analyzed here in detail as an illustration of the general results.

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