Homological Theory of Representations

This book for advanced graduate students and researchers discusses representations of associative algebras and their homological theory.

List of contents

Introduction; Conventions and notations; Glossary; Standard functors and isomorphisms; Part I. Abelian and Derived Categories: 1. Localisation; 2. Abelian categories; 3.Triangulated categories; 4. Derived categories; 5. Derived categories of representations; Part II. Orthogonal Decompositions: 6. Gorenstein algebras, approximations and Serre duality; 7. Tilting in exact categories; 8. Polynomial representations; Part III. Derived Equivalences: 9. Derived equivalences; 10. Examples of derived equivalences; Part IV. Purity: 11. Locally finitely presented categories; 12. Purity; 13. Endofiniteness; 14. Krull-Gabriel dimension; References; Notation; Index.

About the author

Henning Krause is Professor of Mathematics at Bielefeld University. He works in the area of representation theory of finite-dimensional algebras, with a particular interest in homological structures. His previous publications include the Handbook of Tilting Theory (Cambridge, 2007). Professor Krause is Fellow of the American Mathematical Society.

Product details

• Authors: Henning Krause, Henning (Universitat Bielefeld Krause, Krause Henning
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 31.12.2021
• EAN: 9781108838894
• ISBN: 978-1-108-83889-4
• No. of pages: 375
• Series: Cambridge Studies in Advanced Mathematics; Cambridge Studies in Advanced
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, MATHEMATICS / Algebra / General