Book 2004

A Taste of Jordan Algebras

Authors:

ISBN: 978-0-387-95447-9 (Print) 978-0-387-21796-3 (Online)

Table of contents (41 chapters)

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  1. Front Matter

    Pages i-xxv

  2. A Colloquial Survey of Jordan Theory

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      Chapter

      Pages 1-36

      A Colloquial Survey of Jordan Theory

  3. A Historical Survey of Jordan Structure Theory

    1. Front Matter

      Pages 37-38

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      Chapter

      Pages 39-50

      Jordan Algebras in Physical Antiquity: The Search for an Exceptional Setting for Quantum Mechanics

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      Chapter

      Pages 51-68

      Jordan Algebras in the Algebraic Renaissance: Finite-Dimensional Jordan Algebras over Algebraically Closed Fields

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      Chapter

      Pages 69-80

      Jordan Algebras in the Enlightenment: Finite-Dimensional Jordan Algebras over General Fields

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      Chapter

      Pages 81-94

      The Classical Theory: Jordan Algebras with Minimum Condition

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      Chapter

      Pages 95-98

      The Final Classical Formulation: Algebras with Capacity

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      Chapter

      Pages 99-106

      The Classical Methods: Cherchez les Division Idempotents

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      Chapter

      Pages 107-113

      The Russian Revolution: 1977–1983

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      Chapter

      Pages 114-128

      Zel’manov’s Exceptional Methods

  4. The Classical Theory

    1. Front Matter

      Pages 129-131

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      Chapter

      Pages 132-152

      The Category of Jordan Algebras

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      Chapter

      Pages 153-167

      The Category of Alternative Algebras

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      Chapter

      Pages 168-185

      Three Special Examples

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      Chapter

      Pages 186-198

      Jordan Algebras of Cubic Forms

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      Chapter

      Pages 199-210

      Two Basic Principles

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      Chapter

      Pages 211-219

      Inverses

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      Chapter

      Pages 220-234

      Isotopes

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      Chapter

      Pages 235-246

      Peirce Decomposition

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      Chapter

      Pages 247-252

      Off-Diagonal Rules

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      Chapter

      Pages 253-258

      Peirce Consequences

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      Chapter

      Pages 259-267

      Spin Coordinatization

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