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Home > Research > Publications & Outputs > Supplements to maximal subalgebras of Lie algebras
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Supplements to maximal subalgebras of Lie algebras

Research output: Contribution to journalJournal article

Published

Journal publication date10/2013
JournalCommunications in Algebra
Journal number10
Volume41
Number of pages10
Pages3848-3857
Early online date26/07/13
Original languageEnglish

Abstract

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