[[Lie algebras MOC]]
# Simple Lie algebra

A [[Lie algebra]] $\mathfrak{g}$ is said to be **simple** iff it is non-[[Abelian Lie algebra|abelian]] and it has no nontrivial [[Lie algebra ideal]]
(equivalently the [[adjoint Lie algebra representation]] is irreducible).[^1972] #m/def/lie 

  [^1972]: 1972\. [[Sources/@humphreysIntroductionLieAlgebras1972|Introduction to Lie Algebras and Representation Theory]], §2.1, p. 6

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