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arXiv · 1006.5636

The index complex of a maximal subalgebra of a Lie algebra

David A. Towers
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Abstract

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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David A. Towers. 2010-06-29. The index complex of a maximal subalgebra of a Lie algebra. https://arxiv.org/abs/1006.5636

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