Representation Theory

The book "Representation Theory" by Alexander Zimmermann offers a comprehensive introduction to the representation theory of groups and finite-dimensional algebras. It begins with the fundamentals of non-commutative ring theory and covers the necessary background in elementary homological algebra, as well as group representations leading up to block theory. Topics include vertices, defect groups, Green and Brauer correspondences, and Clifford theory. The content is designed to be applicable in a general framework for broader algebraic concepts, particularly for symmetric finite-dimensional algebras over a field.

The book also introduces readers to abelian and derived categories and explains their application to stable module categories, as well as the main invariants and their connections. Numerous methods from the representation theory of algebras are presented, complemented by group-theoretical applications. "Representation Theory" is aimed at students of algebra and is suitable for both self-study and classroom use.