The index complex of a maximal subalgebra of a Lie algebra
Rings and Algebras
2010-06-30 v1 Group Theory
Representation Theory
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.
Keywords
Cite
@article{arxiv.1006.5636,
title = {The index complex of a maximal subalgebra of a Lie algebra},
author = {David A. Towers},
journal= {arXiv preprint arXiv:1006.5636},
year = {2010}
}