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.
Structure of AlgebrasCovers the structure of finite dimensional algebras and the characterization of semisimple algebras.
Linearly reductive groupsDiscusses linearly reductive groups and their properties, focusing on completely reducible representations and equivalent modules.
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.
Modules of CovariantsExplores the decomposition of the circle of the coordinate ring of a G variety into a direct sum of simple submodules.
