from Wiktionary, Creative Commons Attribution/Share-Alike License
- adj. In which each submodule is a direct summand.
- adj. For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree.
- adj. Being a direct sum of simple Lie algebras.
- adj. Being a linear algebraic group whose radical of the identity component is trivial.
The action of a real semisimple lie group on a complex flag manifold, II: Unitary representations on partially holomorphic cohomology spaces by Joseph Albert Wolf
Consider the Lie Algebra of a semisimple algebraic group over a field of characteristic
"generalized Sato-Tate law," and that figuring out which generalized Sato-Tate law applies to a given family amounts essentially to computing a certain complex semisimple (not necessarily connected) algebraic group, the "geometric monodromy group" attached to that family.