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Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups

  • Ludwig Pittner

Part of the Lecture Notes in Physics Monographs book series (LNPMGR, volume 39)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Pages 1-4
  3. Pages 5-41
  4. Pages 43-72
  5. Pages 279-403
  6. Pages 405-431
  7. Back Matter
    Pages 433-469

About this book

Introduction

Quantum groups and quantum algebras as well as non-commutative differential geometry are important in mathematics. They are also considered useful tools for model building in statistical and quantum physics. This book, addressing scientists and postgraduates, contains a detailed and rather complete presentation of the algebraic framework. Introductory chapters deal with background material such as Lie and Hopf superalgebras, Lie super-bialgebras, or formal power series. A more general approach to differential forms, and a systematic treatment of cyclic and Hochschild cohomologies within their universal differential envelopes are developed. Quantum groups and quantum algebras are treated extensively. Great care was taken to present a reliable collection of formulae and to unify the notation, making this volume a useful work of reference for mathematicians and mathematical physicists.

Keywords

differential geometry geometry quantum physics

Authors and affiliations

  • Ludwig Pittner
    • 1
  1. 1.Institut für Theoretische PhysikKarl-Franzens-Universität GrazGrazAustria

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-47801-0
  • Copyright Information Springer Berlin Heidelberg 1996
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-60587-4
  • Online ISBN 978-3-540-47801-0
  • Series Print ISSN 0940-7677
  • Buy this book on publisher's site