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  • Textbook
  • © 2015

Principal Bundles

The Quantum Case

  • Exercises throughout
  • Topics have never been presented in a book written for a general audience of mathematicians and physicists
  • Provides a more intuitive, accessible presentation of the material

Part of the book series: Universitext (UTX)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xv
  2. Introduction

    • Stephen Bruce Sontz
    Pages 1-6
  3. First-Order Differential Calculus

    • Stephen Bruce Sontz
    Pages 7-17
  4. First-Order Differential Calculus of a Hopf Algebra

    • Stephen Bruce Sontz
    Pages 19-36
  5. Adjoint Co-action

    • Stephen Bruce Sontz
    Pages 37-40
  6. Covariant Bimodules

    • Stephen Bruce Sontz
    Pages 41-63
  7. Covariant First-Order Differential Calculi

    • Stephen Bruce Sontz
    Pages 65-105
  8. The Braid Groups

    • Stephen Bruce Sontz
    Pages 107-122
  9. An Interlude: Some Abstract Nonsense

    • Stephen Bruce Sontz
    Pages 123-125
  10. The Braided Exterior Algebra

    • Stephen Bruce Sontz
    Pages 127-137
  11. Higher-Order Differential Calculi

    • Stephen Bruce Sontz
    Pages 139-160
  12. ∗-Structures

    • Stephen Bruce Sontz
    Pages 161-180
  13. Quantum Principal Bundles

    • Stephen Bruce Sontz
    Pages 181-276
  14. Finite Classical Groups

    • Stephen Bruce Sontz
    Pages 277-295
  15. Dunkl Operators as Covariant Derivatives in a QPB

    • Stephen Bruce Sontz
    Pages 297-317
  16. What Next?

    • Stephen Bruce Sontz
    Pages 319-320
  17. Erratum

    • Stephen Bruce Sontz
    Pages E1-E1
  18. Back Matter

    Pages 321-350

About this book

This introductory text is the first book about quantum principal bundles and their quantum connections which are natural generalizations to non-commutative geometry of principal bundles and their connections in differential geometry. To make for a more self-contained book there is also much background material on Hopf algebras, (covariant) differential calculi, braid groups and compatible conjugation operations. The approach is slow paced and intuitive in order to provide researchers and students in both mathematics and physics ready access to the material.

Reviews

“The book contains a lot of exercises of different degree of difficulties, but the proofs of the theorems are done in detail. The book is very elaborate and very welcome not only for graduate students, but also for all people interested in mathematical physics.” (Stefan Berceanu, zbMATH 1358.58002, 2017)

Authors and Affiliations

  • Centro de Investigacion en Matematicas, Guanajuato, Mexico

    Stephen Bruce Sontz

About the author

Stephen Bruce Sontz is a Professor at Centro de Investigacion en Matematicas (CIMAT). He received his Ph.D. from the University of Virginia, USA, in 1994.

Bibliographic Information

  • Book Title: Principal Bundles

  • Book Subtitle: The Quantum Case

  • Authors: Stephen Bruce Sontz

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-319-15829-7

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Softcover ISBN: 978-3-319-15828-0Published: 30 April 2015

  • eBook ISBN: 978-3-319-15829-7Published: 20 April 2015

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XV, 350

  • Topics: Mathematical Physics, Quantum Computing, Quantum Physics

Buy it now

Buying options

eBook USD 29.99 USD 59.99
50% discount Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.99 USD 79.99
50% discount Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access