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Classification of simple weight modules for super-Virasoro algebra with a finite-dimensional weight space

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Abstract

There are two extensions of Virasoro algebra with particular importance in superstring theory: the Ramond algebra and the Neveu-Schwarz algebra, which are ℤ2-graded extensions of the Virasoro algebra. In this paper, we show that the support of a simple weight module over the Ramond algebra with an infinite-dimensional weight space coincides with the weight lattice and that all intersections of non-trivial weight spaces and odd part or even part of the module are infinite-dimensional. This result together with the one that we have obtained over the Neveu-Schwarz algebra generalizes the result for the Virasoro algebra to the super-Virasoro algebras.

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  1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, China

    Xiufu Zhang

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  1. Xiufu Zhang
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Correspondence to Xiufu Zhang.

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Zhang, X. Classification of simple weight modules for super-Virasoro algebra with a finite-dimensional weight space. Front. Math. China 10, 1233–1242 (2015). https://doi.org/10.1007/s11464-015-0466-y

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  • DOI: https://doi.org/10.1007/s11464-015-0466-y

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