A TASTE OF JORDAN ALGEBRAS

By E. FIENY

PART HISTORICAL SURVEY JORDAN STRUCTURE: THEORY JORDAN ALGEBRAS PHYSICAL ANTIQUITY: THE SEARCH FOR EXCEPTIONAL SETTING FOR QUANTUM MECHANICS JORDAN ALGEBRAS THE ALGEBRAIC RENAISSANCE: FINITE-DIMENSIONAL JORDAN ALGEBRAS OVER ALGEBRAICALLY CLOSED FIELDS JORDAN ALGEBRAS 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 ZEL MANOV S EXCEPTIONAL METHODS PART THE CLASSICAL THEORY THE CATEGORY JORDAN ALGEBRAS THE CATEGORY ALTERNATIVE ALGEBRAS THREE SPECIAL EXAMPLES JORDAN ALGEBRAS 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 OSBORN S CAPACITY THEOREM CLASSICAL CLASSIFICATION PART III: ZEL MANOV S EXCEPTIONAL THEOREM THE RADICAL BEGETTING AND BOUNDING IDEMPOTENTS BOUNDED SPECTRA BEGET CAPACITY ABSORBERS INNER IDEALS PRIMITIVITY THE PRIMITIVE HEART FILTERS AND ULTRAFILTERS ULTRAPRODUCTS THE FINAL ARGUMENT