Zhu algebras of superconformal vertex algebras

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 Hamiltonian operators or Virasoro elements, 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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