Handbook of Tilting Theory倾向性理论手册 下载 pdf 百度网盘 epub 免费 2025 电子版 mobi 在线

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 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

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书籍介绍

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.