Homological Theory of Representations

Homological methods are used in modern representation theory, with a focus on module categories of Artin algebras, Gorenstein and quasi-hereditary algebras, and the theory of purity for locally finitely presented categories. This book is essential for advanced graduate students and researchers.

Format: Hardback
Length: 375 pages
Publication date: 18 November 2021
Publisher: Cambridge University Press

Modern developments in representation theory heavily rely on homological methods, which are introduced in this book for advanced graduate students and researchers. The book begins by discussing the categorical foundations, including abelian and derived categories, with an emphasis on localisation, spectra, and purity. The representation theoretic focus then shifts to module categories of Artin algebras, with discussions of the representation theory of finite groups and finite quivers. Additionally, Gorenstein and quasi-hereditary algebras, such as Schur algebras, which model polynomial representations of general linear groups, and the Morita theory of derived categories via tilting objects, are covered. The final part of the book is devoted to a systematic introduction to the theory of purity for locally finitely presented categories, covering pure-injectives, definable subcategories, and Ziegler spectra.

With its clear, detailed exposition of important topics in modern representation theory, many of which were unavailable in one volume until now, this book deserves a place in every representation theorist's library. The book is an essential resource for anyone interested in the field, providing a comprehensive and up-to-date introduction to homological methods and their applications in representation theory.

Weight: 920g
Dimension: 159 x 236 x 38 (mm)
ISBN-13: 9781108838894
Edition number: New ed