Michael Ruzhansky, Ville Turunen
Abstract
In this chapter we study linear Lie groups, i.e., Lie groups which are closed subgroups of GL(n, ℂ). But first some words about the general Lie groups: Definition 8.0.1 (Lie groups). A Lie group is a C∞-manifold which is also a group such that the group operations are C∞-smooth.
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In this chapter we study linear Lie groups, i.e., Lie groups which are closed subgroups of GL(n, ℂ). But first some words about the general Lie groups: Definition 8.0.1 (Lie groups). A Lie group is a C∞-manifold which is also a group such that the group operations are C∞-smooth.
Key concepts: Lie group, Simple Lie group, Representation of a Lie group, Lie theory, Pure mathematics, Adjoint representation, Mathematics, Group of Lie type