Handbook of Tilting Theory倾向性理论手册
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作者： Lidia Angeleri Hügel，Dieter Happel，Henning Krause著
出 版 社：
出版时间： 2007-1-1字数：版次： 1页数： 472印刷时间： 2007/01/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780521680455包装： 平装内容简介
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.
目录
1 Introduction
2 Basic results of classical tilting theory L. Angeleri Hiigel, D. Happel, and H. Krause
REFERENCES
3 Classification of representation-finite algebras and their modules
T. Bruistle
1 Introduction
2 Notation
3 Representation-finite algebras
4 Critical algebras
5 Tame algebras
REFERENCES
4 A spectral sequence analysis of classical tilting func-tors
S. Brenner and M. C. R. Butler
1 Introduction
2 Tilting modules
3 Tilting functors, spectral sequences and filtrations
4 Applications
5 Edge effects, and the case t=2
REFERENCES
5 Derived categories and tilting
B. Keller
1 Introduction
2 Derived categories
3 Derived functors
4 Tilting and derived equivalences
5 Triangulated categories
6 Morita theory for derived categories
7 comparison of t-structures, spectral sequences
8 Algebraic triangulated categories and dg algebras
REFERENCES
6 Hereditary categoriesH. Lenzing
1 Fundamental concepts
2 Examples of hereditary categories
3 Repetitive shape of the derived category
4 Perpendicular categories
5 Exceptional objects
6 Piecewise hereditary algebras and Happel's theorem
7 Derived equivalence of hereditary categories
8 Modules over hereditary algebras
9 Spectral properties of hereditary categories
10 Weighted projective lines
11 Quasitilted algebras
REFERENCES
7 Fourier-Mukai transforms L. Hille and M. Van den Bergh
1 Some background
2 Notations and conventions
3 Basics on Fourier-Mukai transforms
4 The reconstruction theorem
5 Curves and surfaces
6 Threefolds and higher dimensional varieties
7 Non-commutative rings in algebraic geometry
REFERENCES
8 Tilting theory and homologically finite subcategories with applications to quasihereditary algebras
I. Reiten
1 The Basic Ingredients
2 The Correspondence Theorem
3 Quasihereditary algebras and their generalizations
4 Generalizations
REFERENCES
9 Tilting modules for algebraic groups and finite dimensional algebras
S.Donkin
10 Combinatorial aspects of the set of titling modules
L.Unger
11 Infinete dimensional tilting modules and cotorsion pairs
J.Trlifaj
12 Infinite dimensional titing modules over finite dimensional algebras
ф.Solberg
13 Cotiting dualities
R.Colpi and K.R.Fuller
14 Representations of finite groups and tilting
J.Chuang and J.Rickard
15 Morita theory in stable homotopy theory
B.Shipley
Appendix Some remarks concerning tilting modules and tilted algebras. Origin.Relevance.Future
C.M.Ringel
