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.
Diagonalizable GroupsExplores the concept of diagonalizable groups and their properties in linear algebraic groups.
Subgroups and subalgebrasExplores the unique determination of homomorphisms by differentials and the intersection of closed subgroups' Lie algebras.
Modules of CovariantsExplores the decomposition of the circle of the coordinate ring of a G variety into a direct sum of simple submodules.
Weyl character formulaExplores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.
Linearly reductive groupsDiscusses linearly reductive groups and their properties, focusing on completely reducible representations and equivalent modules.
Structure of AlgebrasCovers the structure of finite dimensional algebras and the characterization of semisimple algebras.
