PSI 2018/2019 - Lie Groups and Lie Algebras (Ali)

Motivation and fundamental concepts of group theory. Examples of groups.

Fundamental concepts of represenation theory. Groups and quantum mechanics. Lie groups.

Lie algebras from Lie groups. The adjoint representation. Examples of Lie groups: GL(n,K), SO(n).

Examples of Lie groups continued: SO(m,n), SU(n), Cartan subalgebra, proof of irreducibility of the adjoint representation for simple Lie groups.

Killing metric, Coset manifold, Representation theory of SU(2) Lie algebra, SU(2) tensors.

SU(2) and SU(3) tensors, Young's tableau.