Representation Theory

Alexander Zimmermann works on equivalences between derived module categories, stable module categories, Hochschild cohomology and integral and modular representations of groups.

"The focus of this text is the representation theory of associative algebras and the modular representation theory of finite groups, with an emphasis on the interplay between these two fields. ... the text at hand is aimed at a beginning graduate student without prior exposure to homological algebra. ... Overall, this book is a great repository of theory, developed almost from scratch, with detailed proofs." (Alex S. Dugas, Mathematical Reviews, May, 2016) "This book is intended as a text for first year master students who want to specialize on representation theory, more precisely: representations of finite-dimensional algebras and modular group representations, with special emphasis on homological methods." (Wolfgang Rump, zbMATH 1306.20001, 2015) "The author's intent is to provide an obviously very serious 'introduction to the representation theory of finite groups and finite dimensional algebras via homological algebra.' ... Zimmermann's book is geared to initiates and serious algebraists aiming at research in the indicated area. It is clearly a labor of love and fine scholarship, and should succeed in providing guidance and instruction in a most interesting and intricate subject." (Michael Berg, MAA Reviews, October, 2014)

• Rings, Algebras and Modules.- Modular Representations of Finite Groups.- Abelian and Triangulated Categories.- Morita theory.- Stable Module Categories.- Derived Equivalences.