A Lie group is called semisimple if its Lie algebra is semisimple. For example, the special linear
group 
and special orthogonal group 
(over 
or 
) are semisimple, whereas triangular groups are not.
Semisimple Lie Group
See also
Heisenberg Group, Lie Group, Semisimple Lie AlgebraExplore with Wolfram|Alpha
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 GroupCite this as:
Weisstein, Eric W. "Semisimple Lie Group." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SemisimpleLieGroup.html