$N=2$ supersymmetric structures on classical $W$-algebras

Eric Ragoucy, Arim Song, Uhi Rinn Suh

We describe an $N=2$ supersymmetric Poisson vertex algebra structure of $N=1$ (resp. $N=0$) classical $W$-algebra associated with $\mathfrak{sl}(n+1|n)$ and the odd (resp. even) pr…