Topological GroupsCovers the definition and examples of topological groups, focusing on actions of groups on spaces.
Probability Theory: Lecture 3Explores random variables, sigma algebras, independence, and shift-invariant measures, emphasizing cylinder sets and algebras.
Modules of CovariantsExplores the decomposition of the circle of the coordinate ring of a G variety into a direct sum of simple submodules.
Cohomology: Cross ProductExplores cohomology and the cross product, demonstrating its application in group actions like conjugation.
Homogeneous SpacesExplores formogenic spaces, topological groups, quotients, and rotations on the unit sphere.
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.
