Geodesic
Spinor Types in Infinite Dimensions
Journal of Lie theory, Tome 15 (2005) no. 2, pp. 457-495 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 81R10, 15A66
Mots-clés : Spinors, representations of the CAR, division algebras 
@article{JLT_2005_15_2_JLT_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},
     url = {http://geodesic.mathdoc.fr/item/JLT_2005_15_2_JLT_2005_15_2_a6/}
}
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E. Galina; A. Kaplan; L. Saal . Spinor Types in Infinite Dimensions. Journal of Lie theory, Tome 15 (2005) no. 2, pp. 457-495. http://geodesic.mathdoc.fr/item/JLT_2005_15_2_JLT_2005_15_2_a6/