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Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups

  • Book
  • © 1996

Overview

Authors:
  1. Ludwig Pittner

    1. Institut für Theoretische Physik, Karl-Franzens-Universität Graz, Graz, Austria

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XII
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  2. Introduction

    Pages 1-4

  3. Lie Algebras

    Pages 5-41

  4. Lie Superalgebras

    Pages 43-72

  5. Coalgebras and Z2-Graded Hopf Algebras

    Pages 73-111

  6. Formal Power Series with Homogeneous Relations

    Pages 113-132

  7. Z2-Graded Lie-Cartan Pairs

    Pages 133-190

  8. Real Lie-Hopf Superalgebras

    Pages 191-212

  9. Universal Differential Envelope

    Pages 213-277

  10. Quantum Groups

    Pages 279-403

  11. Categorial Viewpoint

    Pages 405-431

  12. Back Matter

    Pages 433-469
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Keywords

About this book

Quantum groups and quantum algebras as well as non-commutative differential geometry are important in mathematics and considered to be 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. 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.

Authors and Affiliations

  • Institut für Theoretische Physik, Karl-Franzens-Universität Graz, Graz, Austria

    Ludwig Pittner

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