Li filtrations of SUSY vertex algebras
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Publication:6382696
DOI10.1007/S11005-022-01595-2arXiv2111.05734MaRDI QIDQ6382696
Publication date: 10 November 2021
Abstract: Any vertex algebra has a canonical decreasing filtration, called Li filtration, whose associated graded space has a natural structure of a vertex Poisson algebra. In this note, we introduce an analogous filtration for any SUSY vertex algebra, which was introduced by Heluani and Kac as a superfield formalism of a supersymmetric vertex algebra. We prove that the associated graded superspace of our filtration has a structure of SUSY vertex Poisson algebras. We also introduce and discuss related notions, such as Zhu's -Poisson superalgebras, associated superschemes and singular supports, for SUSY vertex algebras.
Virasoro and related algebras (17B68) Vertex operators; vertex operator algebras and related structures (17B69) Infinite-dimensional Lie (super)algebras (17B65) Poisson algebras (17B63)
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