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Klein and conformal superspaces, split algebras and spinor orbits by:2 (Source: Crossref)

    We discuss 𝒩=1 Klein and Klein-conformal superspaces in D=(2,2) space-time dimensions, realizing them in terms of their functor of points over the split composition algebra s. We exploit the observation that certain split forms of orthogonal groups can be realized in terms of matrix groups over split composition algebras. This leads to a natural interpretation of the sections of the spinor bundle in the critical split dimensions D=4,6 and 10 as s2, s2 and 𝕆s2, respectively. Within this approach, we also analyze the non-trivial spinor orbit stratification that is relevant in our construction since it affects the Klein-conformal superspace structure.

    AMSC: 17A35, 17C60, 32C11, 15A66


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