Course content

The course deals with central concepts and methods in the representation theory of associative algebras beyond what is covered in MA3203.

The contents of the course may vary from year to year. Usual topics include the following:

• Auslander-Reiten theory, in particular properties of Auslander-Reiten quivers and the knitting procedure for these. Also the shape of the Auslander-Reiten quivers for certain classes of algebras, for instance hereditary algebras.
• Finite, tame, and wild representation types, including examples of algebras of these. The course may include the classification of all indecomposables for examples of tame algebras like the path algebra of the Kronecker quiver.
• (Versions of) tilting theory, for instance tilting via torsion pairs, tilting as derived equivalences, and or tau-tilting theory. These could either be a means for transferring information from one algebra to another, or combinatorial tool within one module category.

Other subjects may be taken up based on the interest of the lecturer and the participants.

Learning outcome

1. Knowledge. The student can provide definitions of key concepts, formulate and prove main results, and discuss examples of topics covered in the course.
2. Skills. The students can independently analyze representation theoretic questions, including employing standard techniques and searching relevant literature.
3. Competence. The students will be able to participate in scientific discussions, present results, and begin with research in representation theory.

Learning methods and activities

The precise format of the course will vary, but it will require active student participation, including presentations.

The course will be taught as needed, subject to the availability of a teacher.

Recommended previous knowledge

MA3203 Representation theory

MA3204 Homological algebra

Course materials

Will be discussed at the start of the course.