Group Algebra: Maschke's Theorem

This lecture covers Wedderburn's theorem, stating that a finite dimensional simple algebra is a matrix algebra over a division ring. It also discusses endomorphisms of direct sums of simple finite dimensional modules, group algebras of finite groups, and Maschke's theorem. The latter states that a group algebra of a finite group over C is a direct sum of complex matrix algebras. The lecture emphasizes the concept of semisimple representations and their properties.