Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.
Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.
Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
Covers the isotopic decomposition of modules into simple components and their properties.
Explores the decomposition of the circle of the coordinate ring of a G variety into a direct sum of simple submodules.
Explores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.
Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.
Explores the construction of group representations through various methods and provides an illustrative example using the standard representation of sr2 on c2.
