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Superconformal algebras and transitive group actions on quadrics

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Abstract

A classification of “physical” superconformal algebras is given. The list consists of seven algebras: the Virasoro algebra, the Neveu-Schwarz algebra, theN = 2,3 and 4 algebras, the superalgebra of all vector fields on theN = 2 supercircle, and a new algebraCK 6 constructed in [3]. The proof relies heavily on the classification of all connected subgroups ofSO n(C) which act transitively on the quadric (v, v) = 1.

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Authors and Affiliations

  1. Department of Mathematics, MIT, 02139, Cambridge, MA, USA

    Victor G. Kac

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  1. Victor G. Kac
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To Ernest Borisovich Vinberg on his 60th birthday

Partially supported by NSF grant DMS-9622870

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Kac, V.G. Superconformal algebras and transitive group actions on quadrics. Commun. Math. Phys. 186, 233–252 (1997). https://doi.org/10.1007/BF02885680

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  • DOI: https://doi.org/10.1007/BF02885680

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