Representation theory of Lie groups

Harish-Chandra class

In mathematics, Harish-Chandra's class is a class of Lie groups used in representation theory. Harish-Chandra's class contains all semisimple connected linear Lie groups and is closed under natural operations, most importantly, the passage to Levi subgroups. This closure property is crucial for many inductive arguments in representation theory of Lie groups, whereas the classes of semisimple or connected semisimple Lie groups are not closed in this sense. (Wikipedia).

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Related pages

Lie group | Semisimple Lie algebra | Connected space | Exponential map (Lie theory) | Lie algebra | Complexification | Levi decomposition | Linear group | Representation theory