Lie algebras | Representation theory

Principal subalgebra

In mathematics, a principal subalgebra of a complex simple Lie algebra is a 3-dimensional simple subalgebra whose non-zero elements are regular. A finite-dimensional complex simple Lie algebra has a unique conjugacy class of principal subalgebras, each of which is the span of an sl2-triple. (Wikipedia).

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Related pages

Conjugacy class | Sl2-triple | Regular element of a Lie algebra