Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.
Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
Explores the construction of group representations through various methods and provides an illustrative example using the standard representation of sr2 on c2.
Discusses linearly reductive groups and their properties, focusing on completely reducible representations and equivalent modules.
Explores the decomposition of the circle of the coordinate ring of a G variety into a direct sum of simple submodules.
Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.
