Author | McCrimmon, Kevin. author |
---|---|
Title | A Taste of Jordan Algebras [electronic resource] / by Kevin McCrimmon |
Imprint | New York, NY : Springer New York, 2004 |
Connect to | http://dx.doi.org/10.1007/b97489 |
Descript | XXV, 563 p. online resource |
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: 1977โ1983 -- Zelโmanovโs 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 -- Osbornโs Capacity 2 Theorem -- Classical Classification -- Zelโmanovโs 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