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index complex

Proceedings of the Edinburgh Mathematical Society (1)

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The index complex of a maximal subalgebra of a Lie algebra
Part of
- Lie algebras and Lie superalgebras
David A. Towers
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 54 / Issue 2 / June 2011

Published online by Cambridge University Press:

08 April 2011, pp. 531-542
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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 characterizations of solvable and supersolvable Lie algebras.