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

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Spinor Types in Infinite Dimensions

E. Galina, A. Kaplan, and L. Saal

E. Galina, A. Kaplan, and L. Saal
FAMAF-CIEM, Ciudad Universitaria
Universidad Nacional de Córdoba
5000 Córdoba, Argentina

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 non-associative algebras introduced speculatively by Kaplansky.

Keywords: Spinors, Representations of the CAR, Division Algebras

Classification (MSC2000): Primary: 81R10; Secondary: 15A66

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Electronic fulltext finalized on: 20 May 2010. This page was last modified: 4 Jun 2010.

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