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arXiv · 1209.6032

The super W_{1+\infty} algebra with integral central charge

Thomas Creutzig·Andrew R. Linshaw
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Abstract

The Lie superalgebra SD of regular differential operators on the super circle has a universal central extension \hat{SD}. For each c\in C, the vacuum module M_c(\hat{SD}) of central charge c admits a vertex superalgebra structure, and M_c(\hat{SD}) \cong M_{-c}(\hat{SD}). The irreducible quotient V_c(\hat{SD}) of the vacuum module is known as the super W_{1+\infty} algebra. We show that for each integer n>0, V_n(\hat{SD}) has a minimal strong generating set consisting of 4n fields, and we identify it with a W-algebra associated to the purely odd simple root system of gl(n|n). Finally, we realize V_n(\hat{SD}) as the limit of a family of commutant vertex algebras that generically have the same graded character and possess a minimal strong generating set of the same cardinality.

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BibTeXRIS

Thomas Creutzig, Andrew R. Linshaw. 2012-09-26. The super W_{1+\infty} algebra with integral central charge. https://doi.org/10.1090/s0002-9947-2015-06214-x

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