C-Supplemented Subalgebras of Lie Algebras

Details C-Supplemented Subalgebras of Lie Algebras C-Supplemented Subalgebras of Lie Algebras

2007-12-20

arxiv.org/abs/0712.3390v1

Mathematics

Rings and Algebras

9 pages

Scientific paper

A subalgebra $B$ of a Lie algebra $L$ is {\em c-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 {\em c-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.

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