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.
Tensor Product: Bilinear MapsCovers the concept of tensor product in the context of bilinear maps and explores the uniqueness of tensor products.
Isotypic DecompositionCovers the isotopic decomposition of modules into simple components and their properties.
Cohomology: Cross ProductExplores cohomology and the cross product, demonstrating its application in group actions like conjugation.
Linear Forms in Vector SpacesCovers the definition and properties of linear forms in vector spaces, including generating families and direct sums.
Linear Algebra BasicsCovers the basics of linear algebra, including linear maps, bases, and matrix operations.
