Generators of Supersymmetric Classical W-Algebras

Abstract

We describe an N = 2 supersymmetric Poisson vertex algebra structure of N = 1 (resp. N = 0) classical W -algebra associated with sl(n + 1|n) and the odd (resp. even) principal nilpotent element. This N = 2 supersymmetric structure is connected to the principal sl(2|1)-embedding in sl(n + 1|n) superalgebras, which are the only basic Lie superalgebras that admit such a principal embedding.