Linearly reductive groups

Related lectures (31)

Page 3 of 4

Explores the theory of representation of groups and the concept of complete reducibility.

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Covers completely reducible representations, simple modules, semisimple modules, and G-stable submodules.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Explores weight space decomposition and proves that a connected linear algebraic group with all semi-simple elements must be a torus.

Explores the embedding of chi-varieties into vector spaces with linear actions.

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

Explores chain conditions in module theory, emphasizing Noetherian modules and stabilizing sequences of submodules.

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

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.