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arXiv · 2509.13124

Zhu algebras of superconformal vertex algebras

Ryo Sato·Shintarou Yanagida
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Abstract

The purpose of this note is to demonstrate the advantages of Y.-Z.~Huang's definition of the Zhu algebra (Comm.\ Contemp.\ Math., 7 (2005), no.~5, 649--706) for an arbitrary vertex algebra, not necessarily equipped with a Hamiltonian operator or a Virasoro element, by achieving the following two goals: (1) determining the Zhu algebras of $N=1, 2, 3, 4$ and big $N=4$ superconformal vertex algebras, and (2) introducing the Zhu algebras of $N_K=N$ supersymmetric vertex algebras.

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BibTeXRIS

Ryo Sato, Shintarou Yanagida. 2025-09-16. Zhu algebras of superconformal vertex algebras. https://arxiv.org/abs/2509.13124

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