Group Algebra: Maschke's TheoremExplores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.
Group CohomologyCovers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
Rings and Modules: Lecture 1Covers rings, modules, exact sequences, and finitely generated modules in the context of Noetherian and Artinian properties.
Isotypic DecompositionCovers the isotopic decomposition of modules into simple components and their properties.
Tensor Product: Bilinear MapsCovers the concept of tensor product in the context of bilinear maps and explores the uniqueness of tensor products.
Modules of CovariantsExplores the decomposition of the circle of the coordinate ring of a G variety into a direct sum of simple submodules.
