Supplements to maximal subalgebras of Lie algebras

Towers, David A. (2013) Supplements to maximal subalgebras of Lie algebras. Communications in Algebra, 41 (10). pp. 3848-3857. ISSN 0092-7872

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For a Lie algebra L and a subalgebra M of L we say that a subalgebra U of L is a supplement to M in L if L = M +U. We investigate those Lie algebras all of whose maximal subalgebras have abelian supplements, those that have nilpotent supplements, those that have nil supplements, and those that have supplements with the property that their derived algebra is inside the maximal subalgebra being supplemented. For the algebras over an algebraically closed field of characteristic zero in the last three of these classes we find complete descriptions; for those in the first class partial results are obtained.

Item Type:
Journal Article
Journal or Publication Title:
Communications in Algebra
Additional Information:
The final, definitive version of this article has been published in the Journal, Communications in Algebra, 41 (10), 2013, © Informa Plc
Uncontrolled Keywords:
?? lie algebrasmaximal subalgebrasupplementsolvablesupersolvablefrattini ideal.algebraalgebra and number theoryqa mathematics ??
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Deposited On:
21 Apr 2011 08:20
Last Modified:
29 Jun 2024 23:28