Handbook of Tilting Theory

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

• ISBN13: 9780521680455
• ISBN10: 052168045X
• Format: Paperback
• Copyright: 2007-01-29
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Introduction

Basic results of classic tilting theory

Classification of representation-finite algebras and their modules

A spectral sequence analysis of classical tilting functors

Derived categories and tilting

Fourier-Mukai transforms

Tilting theory and homologically finite subcategories with applications to quasihereditary algebras

Tilting modules for algebraic groups and finite dimensional algebras

Combinatorial aspects of the set of tilting modules

Cotilting dualities

Infinite dimensional tilting modules and cotorsion pairs

Infinite dimensional tilting modules over finite dimensional algebras

Representations of finite groups and tilting

Morita theory in stable homotopy theory

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