Lie algebras MOC

Radical of a Lie algebra

The radical of a Lie algebra is the unique maximal solvable ideal of . lie

Proof of uniqueness

Let be a maximal solvable ideal, and let be a solvable ideal. Then by ^P3, is solvable and thus by maximality, whence .

Properties

• is a semisimple Lie algebra iff , which is sometimes taken as a definition.¹

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Footnotes

1. 1972. Introduction to Lie Algebras and Representation Theory, §3.1, p. 11 ↩