Towers, David A.
(2011)
*The index complex of a maximal subalgebra of a Lie algebra.*
Proceedings of the Edinburgh Mathematical Society, 54 (2).
pp. 531-542.
ISSN 0013-0915

Official URL: https://doi.org/10.1017/S0013091509001035

## 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.

Item Type:

Journal Article

Journal or Publication Title:

Proceedings of the Edinburgh Mathematical Society

Additional Information:

http://journals.cambridge.org/action/displayJournal?jid=PEM The final, definitive version of this article has been published in the Journal, Proceedings of The Edinburgh Mathematical Society, 54 (2), pp 531-542 2011, © 2011 Cambridge University Press.

Uncontrolled Keywords:

/dk/atira/pure/researchoutput/libraryofcongress/qa

Subjects:

?? LIE ALGEBRASMAXIMAL SUBALGEBRAINDEX COMPLEXIDEAL INDEXSOLVABLESUPERSOLVABLEFRATTINI IDEAL.MATHEMATICS(ALL)QA MATHEMATICS ??

Departments:

ID Code:

27158

Deposited By:

Deposited On:

05 Oct 2009 14:06

Refereed?:

Yes

Published?:

Published

Last Modified:

20 Sep 2023 00:02