Structure of AlgebrasCovers the structure of finite dimensional algebras and the characterization of semisimple algebras.
Isotypic DecompositionCovers the isotopic decomposition of modules into simple components and their properties.
Lie Algebra: Group TheoryExplores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.
Weyl character formulaExplores the proof of the Weyl character formula for finite-dimensional representations of semisimple 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.
Group CohomologyCovers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
