Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations

  • Authors
  • Stefaan Caenepeel
  • Gigel Militaru
  • Shenglin Zhu

Part of the Lecture Notes in Mathematics book series (LNM, volume 1787)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 3-37
  3. Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 39-87
  4. Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 89-157
  5. Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 159-213
  6. Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 217-243
  7. Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 245-300
  8. Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 301-316
  9. Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 317-343
  10. Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 345-352
  11. Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 353-354
  12. Back Matter
    Pages 355-355

About this book

Introduction

Doi-Koppinen Hopf modules and entwined modules unify various kinds of modules that have been intensively studied over the past decades, such as Hopf modules, graded modules, Yetter-Drinfeld modules. The book presents a unified theory, with focus on categorical concepts generalizing the notions of separable and Frobenius algebras, and discussing relations with smash products, Galois theory and descent theory. Each chapter of Part II is devoted to a particular nonlinear equation. The exposé is organized in such a way that the analogies between the four are clear: the quantum Yang-Baxter equation is related to Yetter-Drinfeld modules, the pentagon equation to Hopf modules, and the Long equation to Long dimodules. The Frobenius-separability equation provides a new viewpoint to Frobenius and separable algebras.

Keywords

Entwined module Frobenius functor Galois theory Nonlinear equation Separable functor Yetter-Drinfeld module algebra equation

Bibliographic information

  • DOI https://doi.org/10.1007/b83849
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-43782-6
  • Online ISBN 978-3-540-48042-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book