Journal of Lie Theory Vol. 15, No. 2, pp. 457–495 (2005) 

Spinor Types in Infinite DimensionsE. Galina, A. Kaplan, and L. Saal%E. Galina, A. Kaplan, and L. Saal FAMAFCIEM, Ciudad Universitaria Universidad Nacional de Córdoba 5000 Córdoba, Argentina galina@mate.uncor.edu kaplan@mate.uncor.edu saal@mate.uncor.edu Abstract: 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 nonassociative algebras introduced speculatively by Kaplansky. Keywords: Spinors, Representations of the CAR, Division Algebras Classification (MSC2000): Primary: 81R10; Secondary: 15A66 Full text of the article: (for faster download, first choose a mirror)
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