Lectures related to Diagonalizable Groups

Explores various directions for studying algebraic groups and offers references for further exploration.

Introduces characters as group homomorphisms from linear algebraic groups to multiplicative groups.

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Explores automorphism groups of trees and graphs, including actions on trees and group homomorphisms.

Explores the decomposition of the circle of the coordinate ring of a G variety into a direct sum of simple submodules.

Explores the differential of group actions on vector spaces and the behavior of orbit maps.

Introduces the regular representation, a key tool for studying group actions on varieties.

Explores the Hopf formula in cohomology groups, emphasizing the 4-term exact sequence and its implications.

Explores the torus, linear groups, stability properties of matrices, and homomorphisms.