Supersymmetric W-algebras

We explain 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 gl ( n + 1 | n ) .