maximal ideal in Lie algebra

Question

suppose that $L$ is leibniz or lie algebra and $M$ is maximal ideal of this.then $L/M$ is simple or one dimensional.why say that one dimensional?

score 1 · Answer 1 · answered Dec 02 '16 at 16:15

1

$L/M$ is simple. a 1-dimensional Lie algebra is simple.

answered Dec 02 '16 at 16:15

Tsemo Aristide

Have you checked the other answer? For me, yours doesn't make much sense since, as already said above, commutative Lie algebras are not usually considered simple (they have vanishing Killing form, among others). Therefore this post doesn't really look like an answer, you might want to consider deleting it. – Alex M. Dec 04 '16 at 14:14

score 1 · Accepted Answer · answered Dec 02 '16 at 16:21

1

A simple Lie algebra is usually defined to be non-abelian, so a one-dimensional Lie algebra would not usually be considered to be simple.

answered Dec 02 '16 at 16:21

David Towers

:then every simple and abelian Lie algebra have one-dimensional? – pink floyd Dec 02 '16 at 17:15
No, an abelian Lie algebra is not simple. So L/M is EITHER simple OR one-dimensional. The smallest simple Lie algebra is three dimensional. – David Towers Dec 02 '16 at 18:45

2 Answers2