Handbook of Tilting Theory

ISBN-13: 9780521680455 / Angielski / Miękka / 2007 / 484 str.

Lidia Angeleri Hugel; Dieter Happel; Henning Krause

Opis

Tilting theory originates in the representation theory of finite dimensional algebras. Today the subject is of much interest in various areas of mathematics, such as finite and algebraic group theory, commutative and non-commutative algebraic geometry, and algebraic topology. The aim of this book is to present the basic concepts of tilting theory as well as the variety of applications. It contains a collection of key articles, which together form a handbook of the subject, and provide both an introduction and reference for newcomers and experts alike.

Recenzje

'In my view, the editors have succeeded in choosing a balanced selection of topics and in finding appropriate authors for the various sections. The book is seeded with a plenitude of references and will certainly be a valuable guide both for established researchers and newcomers to the field.' Bulletin of the London Mathematical Society

Spis treści

1. Introduction; 2. Basic results of classic tilting theory L. Angeleri Hügel, D. Happel and H. Krause; 3. Classification of representation-finite algebras and their modules T. Brüstle; 4. A spectral sequence analysis of classical tilting functors S. Brenner and M. C. R. Butler; 5. Derived categories and tilting B. Keller; 6. Fourier-Mukai transforms L. Hille and M. Van den Bergh; 7. Tilting theory and homologically finite subcategories with applications to quasihereditary algebras I. Reiten; 8. Tilting modules for algebraic groups and finite dimensional algebras S. Donkin; 9. Combinatorial aspects of the set of tilting modules L. Unger; 10. Cotilting dualities R. Colpi and K. R. Fuller; 11. Infinite dimensional tilting modules and cotorsion pairs J. Trlifaj; 12. Infinite dimensional tilting modules over finite dimensional algebras Ø. Solberg; 13. Representations of finite groups and tilting J. Chuang and J. Rickard; 14. Morita theory in stable homotopy theory B. Shipley.