Schur's Lemma and Representations

This lecture covers Schur's lemma and its applications in the context of representations of an associative algebra over an algebraically closed field. It discusses the concept of irreducibility, homomorphisms of representations, and the properties of intertwiners. The lecture also explores examples of representations, including the left regular representation and the polynomial algebra. Additionally, it delves into the implications of Schur's lemma in the context of countably dimensional representations and provides insights into the uniqueness and isomorphism of representations.