Semisimple Lie Group

A Lie group is called semisimple if its Lie algebra is semisimple. For example, the special linear group 👁 SL(n)
and special orthogonal group 👁 SO(n)
(over 👁 R
or 👁 C
) are semisimple, whereas triangular groups are not.

See also

Heisenberg Group, Lie Group, Semisimple Lie Algebra

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References

Knapp, A. W. "Group Representations and Harmonic Analysis, Part II." Not. Amer. Math. Soc. 43, 537-549, 1996.Varadarajan, V. S. Lie Groups, Lie Algebras, and Their Representations. New York: Springer-Verlag, 1984.

Referenced on Wolfram|Alpha

Semisimple Lie Group

Cite this as:

Weisstein, Eric W. "Semisimple Lie Group." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SemisimpleLieGroup.html

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