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.
Definition.
A Lie group "G" with the Lie algebra "g" is said to be in Harish-Chandra's class if it satisfies the following conditions: