Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 15 (2005), No. 2, 457--495Copyright Heldermann Verlag 2005 Spinor Types in Infinite Dimensions Esther Galina FAMAF-CIEM, Ciudad Universitaria, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina galina@mate.uncor.edu Aroldo Kaplan FAMAF-CIEM, Ciudad Universitaria, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina kaplan@mate.uncor.edu Linda Saal FAMAF-CIEM, Ciudad Universitaria, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina saal@mate.uncor.edu [Abstract-pdf] The Cartan-Dirac classification of spinors into types is generalized to infinite dimensions. The main conclusion is that, in the statistical interpretation where such spinors are functions on $\Bbb Z_2^\infty$, any real or quaternionic structure involves switching zeroes and ones. There results a maze of equivalence classes of each type. Some examples are shown in $L^2({\Bbb T})$. The classification of spinors leads to a parametrization of certain non-associative algebras introduced speculatively by Kaplansky. Keywords: Spinors, representations of the CAR, division algebras. MSC: 81R10; 15A66 [ Fulltext-pdf  (313  KB)] for subscribers only.