Advertisement

Real Spinorial Groups

A Short Mathematical Introduction

  • Sebastià Xambó-Descamps

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-x
  2. Sebastià Xambó-Descamps
    Pages 1-21
  3. Sebastià Xambó-Descamps
    Pages 23-40
  4. Sebastià Xambó-Descamps
    Pages 41-61
  5. Sebastià Xambó-Descamps
    Pages 63-76
  6. Sebastià Xambó-Descamps
    Pages 77-106
  7. Sebastià Xambó-Descamps
    Pages 107-135
  8. Back Matter
    Pages 137-151

About this book

Introduction

This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they relate to the group of isometries of that geometry.

After a concise mathematical introduction, it offers an axiomatic presentation of the geometric algebra of an orthogonal geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions), it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. Lastly, the book provides pointers to major applications, an extensive bibliography and an alphabetic index.

Combining the characteristics of a self-contained research monograph and a state-of-the-art survey, this book is a valuable foundation reference resource on applications for both undergraduate and graduate students.

Keywords

orthogonal geometry geometric algebra orthogonal groups spinorial groups geometric covariance

Authors and affiliations

  • Sebastià Xambó-Descamps
    • 1
  1. 1.Universitat Politècnica de CatalunyaBarcelonaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-00404-0
  • Copyright Information The Author(s), under exclusive licence to Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-00403-3
  • Online ISBN 978-3-030-00404-0
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site
Industry Sectors
Aerospace
Oil, Gas & Geosciences