Algebraic operad of SUSY Poisson vertex algebra

Abstract

As a continuation of our study (Y.N., S.Y., arXiv:2209.14617) on the algebraic operad of SUSY vertex algebras, we introduce the SUSY coisson operad, which encodes the structures of SUSY Poisson vertex algebras. Our operad is a natural SUSY analogue of the operad encoding the structures of Poisson vertex algebras introduced by Bakalov, De Sole, Heluani and Kac (2019). We also give an embedding of the associated graded of the SUSY chiral operad into the SUSY coisson operad in the filtered case.