Definitions

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.

Etymologies

semi- +‎ simple (Wiktionary)

Examples

  • 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

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  • Consider the Lie Algebra of a semisimple algebraic group over a field of characteristic

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  • "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.

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