Supersymmetric \(W\)-algebras

Alexander Molev, Eric Ragoucy and Uhi Rinn Suh

Abstract

We develop a general theory of \(W\)-algebras in the context of supersymmetric vertex algebras. We describe the structure of \(W\)-algebras associated with odd nilpotent elements of Lie superalgebras in terms of their free generating sets. As an application, we produce explicit free generators of the \(W\)-algebra associated with the odd principal nilpotent element of the Lie superalgebra \({\mathfrak{gl}}(n+1|n)\).