Handbook of Tilting Theory

A handbook of key articles providing both an introduction and reference for newcomers and experts alike.

Lidia Angeleri Hügel (Edited by), Dieter Happel (Edited by), Henning Krause (Edited by)

9780521680455, Cambridge University Press

Paperback, published 4 January 2007

484 pages, 45 b/w illus. 1 table
22.8 x 15.2 x 2.5 cm, 0.755 kg

'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

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.

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.

Subject Areas: Topology [PBP], Geometry [PBM], Algebra [PBF]