Semisimple Lie groups are a class of Lie groups that are characterized by their associated Lie algebras being semisimple. This means that the Lie algebra can be decomposed into a direct sum of simple Lie algebras, which are non-abelian and cannot be further decomposed. These groups play a crucial role in the study of homogeneous spaces, as they provide a structure that allows for rich geometric and algebraic properties.
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