Semisimple algebraic group

In mathematics, especially in the areas of abstract algebra and algebraic geometry studying linear algebraic groups, a semisimple algebraic group is a type of matrix group which behaves much like a semisimple Lie algebra or semisimple ring.


A linear algebraic group is called semisimple if and only if the (solvable) radical of the identity component is trivial.

Equivalently, a semisimple linear algebraic group has no non-trivial connected, normal, abelian subgroups.




This article is issued from Wikipedia - version of the 5/13/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.