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A Taste of Jordan Algebras

  • Kevin McCrimmon

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xxv
  2. A Colloquial Survey of Jordan Theory

  3. A Historical Survey of Jordan Structure Theory

  4. The Classical Theory

    1. Front Matter
      Pages 129-131
    2. Pages 168-185
    3. Pages 199-210
    4. Pages 211-219
    5. Pages 220-234
    6. Pages 235-246
    7. Pages 247-252
    8. Pages 253-258
    9. Pages 259-267
    10. Pages 301-307
    11. Pages 308-311
    12. Pages 318-324
    13. Pages 325-329
    14. Pages 330-334
    15. Pages 356-358
  5. Zel’manov’s Exceptional Theorem

    1. Front Matter
      Pages 359-361
    2. Pages 362-380
    3. Pages 410-421
    4. Pages 422-426
    5. Pages 427-432
    6. Pages 433-439
    7. Pages 440-443
  6. Back Matter
    Pages 445-562

About this book

Introduction

 In this book, Kevin McCrimmon describes the history of Jordan Algebras and he describes in full mathematical detail the recent structure theory for Jordan algebras of arbitrary dimension due to Efim Zel'manov. To keep the exposition elementary, the structure theory is developed for linear Jordan algebras, though the modern quadratic methods are used throughout. Both the quadratic methods and the Zelmanov results go beyond the previous textbooks on Jordan theory, written in the 1960's and 1980's before the theory reached its final form.

This book is intended for graduate students and for individuals wishing to learn more about Jordan algebras. No previous knowledge is required beyond the standard first-year graduate algebra course. General students of algebra can profit from exposure to nonassociative algebras, and students or professional mathematicians working in areas such as Lie algebras, differential geometry, functional analysis, or exceptional groups and geometry can also profit from acquaintance with the material. Jordan algebras crop up in many surprising settings and can be applied to a variety of mathematical areas.

Kevin McCrimmon introduced the concept of a quadratic Jordan algebra and developed a structure theory of Jordan algebras over an arbitrary ring of scalars. He is a Professor of Mathematics at the University of Virginia and the author of more than 100 research papers.

Keywords

algebra associative algebra lie algebra linear algebra matrices matrix quadratic form

Authors and affiliations

  • Kevin McCrimmon
    • 1
  1. 1.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

Bibliographic information