The index complex of a maximal subalgebra of a Lie algebra

Details The index complex of a maximal subalgebra of a Lie algebra The index complex of a maximal subalgebra of a Lie algebra

2010-06-29

arxiv.org/abs/1006.5636v1

Mathematics

Rings and Algebras

Scientific paper

Let M be a maximal subalgebra of the Lie algebra L. A subalgebra C of L is said to be a completion for M if C is not contained in M but every proper subalgebra of C that is an ideal of L is contained in M. The set I(M) of all completions of M is called the index complex of M in L. We use this concept to investigate the influence of the maximal subalgebras on the structure of a Lie algebra, in particular finding new characterisations of solvable and supersolvable Lie algebras.

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