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