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Supplements to maximal subalgebras of Lie algebras

Research output: Contribution to journalJournal article


<mark>Journal publication date</mark>10/2013
<mark>Journal</mark>Communications in Algebra
Issue number10
Number of pages10
Pages (from-to)3848-3857
Early online date26/07/13
<mark>Original language</mark>English


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.

Bibliographic note

The final, definitive version of this article has been published in the Journal, Communications in Algebra, 41 (10), 2013, © Informa Plc