Simple Lie algebra

Note: This draft, when it becomes matured and informative, will replace the current redirect simple Lie algebra (see Talk:Simple_Lie_algebra for the reason why this page should start as a draft.)

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In algebra, a simple Lie algebra is a Lie algebra that (i) is not abelian and (ii) contains no nontrivial proper ideals. The classification of real simple Lie algebras is one of major achievements of Wilhelm Killing and Élie Cartan.

Simple complex Lie algebra

A finite-dimensional simple complex Lie algebra is isomorphic to either of the following: ${\mathfrak {sl}}_{n}\mathbb {C}$, ${\mathfrak {so}}_{n}\mathbb {C}$, ${\mathfrak {sp}}_{2n}\mathbb {C}$ (classical Lie algebras) or one of the five exceptional Lie algebras.

See also

• Simple Lie group
• Satake diagram

References

• Jacobson, Nathan, Lie algebras, Republication of the 1962 original. Dover Publications, Inc., New York, 1979. ISBN 0-486-63832-4
• Chapter X of Jacobson (1962) considers a classification of simple Lie algebras over a field of characteristic zero.

Category:Lie algebras