Prerequisites for the summer school

July 30 – August 3, 2019

Familiarity with the following concepts might turn out to be useful during the summer school and help you to understand the lectures.

Representation theory Algebras and modules, quivers, representations, Auslander–Reiten theory, hereditary algebras, triangulated categories in representation theory.

• Ibrahim Assem, Andrzej Skowroński, and Daniel Simson. Elements of the representation theory of associative algebras. Volume 1: Techniques of representation theory, 2006.

• Maurice Auslander, Idun Reiten, and Sverre O. Smalø. Representation theory of Artin algebras, 1997.

• Dieter Happel. Triangulated categories in the representation of finite dimensional algebras, 1988.
Homological algebra Abelian categories, derived functors, Ext, Tor, chain complexes, (co)homologies, triangulated categories, derived categories, homotopy categories.

• Charles A. Weibel. An introduction to homological algebra, 1994.

• Sergei I. Gelfand, and Yuri I. Manin. Methods of homological algebra, 2003.
Category theory Categories, functors, natural transformations, limits, adjoints.

• Saunders Mac Lane. Categories for the working mathematician, 1998.

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