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C-Supplemented Subalgebras of Lie Algebras.

Research output: Contribution to journalJournal article

Published

Journal publication date2008
JournalJournal of Lie Theory
Journal number3
Volume18
Number of pages8
Pages717-724
Original languageEnglish

Abstract

A subalgebra $B$ of a Lie algebra $L$ is c-{\it supplemented} in $L$ if there is a subalgebra $C$ of $L$ with $L = B + C$ and $B \cap C \leq B_L$, where $B_L$ is the core of $B$ in $L$. This is analogous to the corresponding concept of a c-supplemented subgroup in a finite group. We say that $L$ is c-{\it supplemented} if every subalgebra of $L$ is c-supplemented in $L$. We give here a complete characterisation of c-supplemented Lie algebras over a general field.