Back Sous-groupe compact maximal French Максимальная компактная подгруппа Russian Максимальна компактна підгрупа Ukrainian 极大紧子群 Chinese
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.
Maximal compact subgroups play an important role in the classification of Lie groups and especially semi-simple Lie groups. Maximal compact subgroups of Lie groups are not in general unique, but are unique up to conjugation – they are essentially unique.