Journal of Lie Theory

no. 2
Spinor Types in Infinite Dimensions
Journal of Lie Theory, Volume 15 (2005) no. 2, pp. 457-495
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.
DOI: 10.5802/jolt.386
Classification: 81R10, 15A66
Keywords: Spinors, representations of the CAR, division algebras 
@article{JOLT_2005_15_2_a6,
     author = {E. Galina and A. Kaplan and L. Saal},
     title = {Spinor {Types} in {Infinite} {Dimensions}},
     journal = {Journal of Lie Theory},
     pages = {457--495},
     year = {2005},
     volume = {15},
     number = {2},
     doi = {10.5802/jolt.386},
     zbl = {1133.81034},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.386/}
}
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E. Galina; A. Kaplan; L. Saal. Spinor Types in Infinite Dimensions. Journal of Lie Theory, Volume 15 (2005) no. 2, pp. 457-495. doi: 10.5802/jolt.386

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