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Handbook of Tilting Theory

Handbook of Tilting Theory


Part of London Mathematical Society Lecture Note Series

L. Angeleri Hügel, D. Happel, H. Krause,T. Brüstle, S. Brenner, M. C. R. Butler, B. Keller, L. Hille, M. Van den Bergh, I. Reiten, S. Donkin, L. Unger, R. Colpi, K. R. Fuller, J. Trlifaj, Ø. Solberg, J. Chuang, J. Rickard, B. Shipley
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  • Date Published: January 2007
  • availability: Available
  • format: Paperback
  • isbn: 9780521680455

£ 76.99

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About the Authors
  • 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.

    • Comprehensive treatment of the subject, from basic results through to applications
    • Contributors of the highest calibre cover up-to-date results
    • Ideal for self-teaching and as a reference or handbook
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    Reviews & endorsements

    '… presents a key and very active part of contemporary representation theory in a concise but complete way. It will be indispensible for a wide audience, from graduate students to active researchers in algebra, geometry and topology.' European Mathematical Society Newsletter

    '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

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    Product details

    • Date Published: January 2007
    • format: Paperback
    • isbn: 9780521680455
    • length: 484 pages
    • dimensions: 228 x 152 x 25 mm
    • weight: 0.755kg
    • contains: 45 b/w illus. 1 table
    • availability: Available
  • 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.

  • Editors

    Lidia Angeleri Hügel, Università degli Studi dell'Insubria, Italy

    Dieter Happel, Technische Universität Chemnitz, Germany

    Henning Krause, Universität-Gesamthochschule Paderborn, Germany


    L. Angeleri Hügel, D. Happel, H. Krause,T. Brüstle, S. Brenner, M. C. R. Butler, B. Keller, L. Hille, M. Van den Bergh, I. Reiten, S. Donkin, L. Unger, R. Colpi, K. R. Fuller, J. Trlifaj, Ø. Solberg, J. Chuang, J. Rickard, B. Shipley

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