Lie algebras MOC

Radical of a Lie algebra

The radical of a Lie algebra is the unique maximal solvable ideal of . #m/def/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

#state/tidy | #lang/en | #SemBr

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