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Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations

  • Book
  • © 2002

Overview

Authors:
  1. Stefaan Caenepeel
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    You can also search for this author in PubMed   Google Scholar

  2. Gigel Militaru
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  3. Shenglin Zhu
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1787)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XIV
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  2. 1. Generalities

    • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 3-37

  3. 2. Doi-Koppinen Hopf modules and entwined modules

    • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 39-87

  4. 3. Frobenius and separable functors for entwined modules

    • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 89-157

  5. 4. Applications

    • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 159-213

  6. 5. Yetter-Drinfeld modules and the quantum Yang-Baxter equation

    • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 217-243

  7. 6. Hopf modules and the pentagon equation

    • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 245-300

  8. 7. Long dimodules and the Long equation

    • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 301-316

  9. 8. The Frobenius-Separability equation

    • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 317-343

  10. References

    • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 345-352

  11. Index

    • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
    Pages 353-354

  12. Back Matter

    Pages 355-355
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations

  • Authors: Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b83849

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2002

  • Softcover ISBN: 978-3-540-43782-6Published: 23 July 2002

  • eBook ISBN: 978-3-540-48042-6Published: 13 October 2004

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIV, 354

  • Topics: Associative Rings and Algebras

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