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Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups

  • Textbook
  • © 1994

Overview

Authors:
  1. Alexander J. Hahn

    1. Department of Mathematics, University of Notre Dame, Notre Dame, USA

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Part of the book series: Universitext (UTX)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    • Alexander J. Hahn
    Pages 1-2

  3. Notation and Terminology

    • Alexander J. Hahn
    Pages 3-4

  4. Fundamental Concepts in the Theory of Algebras

    • Alexander J. Hahn
    Pages 5-17

  5. Separable Algebras

    • Alexander J. Hahn
    Pages 18-28

  6. Groups of Free Quadratic Algebras

    • Alexander J. Hahn
    Pages 29-44

  7. Bilinear and Quadratic Forms

    • Alexander J. Hahn
    Pages 45-64

  8. Clifford Algebras: The Basics

    • Alexander J. Hahn
    Pages 65-76

  9. Algebras with Standard Involution

    • Alexander J. Hahn
    Pages 77-91

  10. Arf Algebras and Special Elements

    • Alexander J. Hahn
    Pages 92-105

  11. Consequences of the Existence of Special Elements

    • Alexander J. Hahn
    Pages 106-122

  12. Structure of Clifford and Arf Algebras

    • Alexander J. Hahn
    Pages 123-136

  13. The Existence of Special Elements

    • Alexander J. Hahn
    Pages 137-152

  14. Matrix Theory of Clifford Algebras over Fields

    • Alexander J. Hahn
    Pages 153-171

  15. Dis(R) and Qu(R)

    • Alexander J. Hahn
    Pages 172-193

  16. Brauer Groups and Witt Groups

    • Alexander J. Hahn
    Pages 194-222

  17. The Arithmetic of Wq(R)

    • Alexander J. Hahn
    Pages 223-248

  18. Applications of Clifford Modules

    • Alexander J. Hahn
    Pages 249-265

  19. Back Matter

    Pages 267-287
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Keywords

About this book

Quadratic Algebras, Clifford Algebras, and Arithmetic Forms introduces mathematicians to the large and dynamic area of algebras and forms over commutative rings. The book begins very elementary and progresses gradually in its degree of difficulty. Topics include the connection between quadratic algebras, Clifford algebras and quadratic forms, Brauer groups, the matrix theory of Clifford algebras over fields, Witt groups of quadratic and symmetric bilinear forms. Some of the new results included by the author concern the representation of Clifford algebras, the structure of Arf algebra in the free case, connections between the group of isomorphic classes of finitely generated projectives of rank one and arithmetic results about the quadratic Witt group.

Authors and Affiliations

  • Department of Mathematics, University of Notre Dame, Notre Dame, USA

    Alexander J. Hahn

Bibliographic Information

  • Book Title: Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups

  • Authors: Alexander J. Hahn

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4684-6311-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1994

  • Softcover ISBN: 978-0-387-94110-3Published: 17 December 1993

  • eBook ISBN: 978-1-4684-6311-8Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XI, 286

  • Topics: Algebra

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