Representation Theory

The course is a continuation of MA3201 Rings and modules. It is mainly concerned with discussing finite dimensional algebras over a field. The content of the course may vary, but the core will consist of representations of quivers, path algebras, artinian, noetherian and local rings, projective and injective modules, the Jordan-Hölder Theorem and the Krull-Remak-Schmidt Theorem, radical and socle of modules and rings, exact sequences, categories, functors, equivalence, duality, and almost split sequences.

1. Knowledge: The student masters the connection between module theory over finite dimensional algebras and representations of quivers. The student has basic knowledge of categories, functors, radical, base, exact sequences, and almost split sequences. The student understands the Jordan-Hölder theorem and the Krull-Schmidt theorem.

2. Skills: The student is able to find radicals, bases etc. for special classes of finite dimensional algebras. The student is able to describe the corresponding module if a representation is given, and vice versa. The student is able to compute the indecomposable projective and indecomposable injective representations for a finite dimensional algebra. The student can find the projective cover and injective envelope of a representation.

Lectures/video lectures and problem sessions.