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Some remarks on associated varieties of vertex operator superalgebras

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Abstract

We study several families of vertex operator superalgebras from a jet (super)scheme point of view. We provide new examples of vertex algebras which are “chiral-quantizations" of their \(C_{2}\)-algebras \(R_V\). Our examples come from affine \(C_\ell ^{(1)}\)-series vertex algebras, \(\ell \geqslant 1\), certain \(N=1\) superconformal vertex algebras, Feigin–Stoyanovsky principal subspaces, Feigin–Stoyanovsky type subspaces, graph vertex algebras \(W_{\Gamma }\), and extended Virasoro vertex algebras. We also give a counterexample to the chiral-quantization property for the \(N=2\) superconformal vertex algebra with central charge 1.

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Acknowledgements

The author would like to thank his supervisor, Antun Milas, for reading the manuscript, lots of advice and discussions. He is also grateful to anonymous referees for lots of suggestions on polishing this paper.

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  1. Department of Mathematics and Statistics, SUNY-Albany, Albany, NY, 12222, USA

    Hao Li

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The author was supported by NSF grant NSF-DMS 1601070 of Antun Milas.

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Li, H. Some remarks on associated varieties of vertex operator superalgebras. European Journal of Mathematics 7, 1689–1728 (2021). https://doi.org/10.1007/s40879-021-00477-6

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