Principal subalgebra

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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.

References

• Bourbaki, Nicolas (2005) [1975], Lie groups and Lie algebras. Chapters 7–9, Elements of Mathematics (Berlin), Berlin, New York: Springer-Verlag, ISBN 978-3-540-68851-8, MR 2109105

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