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

Explore with Wolfram|Alpha


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 Web Resource.

Subject classifications