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.

References

• https://aiolatest.com/application-of-abstract-algebra-in-real-life/
• 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