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