High Quality Content by WIKIPEDIA articles! In mathematics, a maximal compact subgroup K of a topological group G is a subgroup K that is a compact space, in the subspace topology, and maximal amongst such subgroups. A maximal compact subgroup does not always exist for a general Lie group, but does exist for a semisimple Lie group, and they play an important role in their theory. Maximal compact subgroups are not in general unique, but are unique up to conjugation – they are essentially unique.

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