Del 195 i serien Cambridge Studies in Advanced Mathematics

Homological Theory of Representations

Inbunden, Engelska, 2021

1 149 kr

Beställningsvara. Skickas inom 7-10 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

Modern developments in representation theory rely heavily on homological methods. This book for advanced graduate students and researchers introduces these methods from their foundations up and discusses several landmark results that illustrate their power and beauty. Categorical foundations include abelian and derived categories, with an emphasis on localisation, spectra, and purity. The representation theoretic focus is on module categories of Artin algebras, with discussions of the representation theory of finite groups and finite quivers. Also covered are Gorenstein and quasi-hereditary algebras, including Schur algebras, which model polynomial representations of general linear groups, and the Morita theory of derived categories via tilting objects. The final part 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, it deserves a place in every representation theorist's library.

Produktinformation

Utgivningsdatum2021-11-18
Mått159 x 236 x 38 mm
Vikt930 g
FormatInbunden
SpråkEngelska
SerieCambridge Studies in Advanced Mathematics
Antal sidor518
FörlagCambridge University Press
ISBN9781108838894

Tillhör följande kategorier

Algebra inom Naturvetenskap och teknik

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.