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A Taste of Jordan Algebras

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 Jorda...

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Bibliographic Details
Main Author: McCrimmon, Kevin. (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic
Language:English
Published: New York, NY : Springer New York, 2004.
Series:Universitext
Subjects:
Mathematics.
Algebra.
Online Access:View fulltext via EzAccess
Table of Contents:
  • A Colloquial Survey of Jordan Theory
  • A Colloquial Survey of Jordan Theory
  • A Historical Survey of Jordan Structure Theory
  • Jordan Algebras in Physical Antiquity: The Search for an Exceptional Setting for Quantum Mechanics
  • Jordan Algebras in the Algebraic Renaissance: Finite-Dimensional Jordan Algebras over Algebraically Closed Fields
  • Jordan Algebras in the Enlightenment: Finite-Dimensional Jordan Algebras over General Fields
  • The Classical Theory: Jordan Algebras with Minimum Condition
  • The Final Classical Formulation: Algebras with Capacity
  • The Classical Methods: Cherchez les Division Idempotents
  • The Russian Revolution: 1977Ớ<U+001c>1983
  • ZelỚ"manovỚ"s Exceptional Methods
  • The Classical Theory
  • The Category of Jordan Algebras
  • The Category of Alternative Algebras
  • Three Special Examples
  • Jordan Algebras of Cubic Forms
  • Two Basic Principles
  • Inverses
  • Isotopes
  • Peirce Decomposition
  • Off-Diagonal Rules
  • Peirce Consequences
  • Spin Coordinatization
  • Hermitian Coordinatization
  • Multiple Peirce Decompositions
  • Multiple Peirce Consequences
  • Hermitian Symmetries
  • The Coordinate Algebra
  • Jacobson Coordinatization
  • Von Neumann Regularity
  • Inner Simplicity
  • Capacity
  • Herstein-Kleinfeld-Osborn Theorem
  • OsbornỚ"s Capacity 2 Theorem
  • Classical Classification
  • ZelỚ"manovỚ"s Exceptional Theorem
  • The Radical
  • Begetting and Bounding Idempotents
  • Bounded Spectra Beget Capacity
  • Absorbers of Inner Ideals
  • Primitivity
  • The Primitive Heart
  • Filters and Ultrafilters
  • Ultraproducts
  • The Final Argument.

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