Homological Theory of Representations

ISBN-13: 9781108838894 / Angielski / Twarda / 2021 / 375 str.

Henning Krause

Opis

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

Recenzje

'Krause's book is a tour de force, providing the current state-of-the-art methodology in homological algebra as it pertains to representation theory … this book is a gem.' James Turner, MAA Reviews

Spis treści

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.