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.
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.
Lie Algebra: Group TheoryExplores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.
Cohomology: Cross ProductExplores cohomology and the cross product, demonstrating its application in group actions like conjugation.
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.
Group CohomologyCovers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
