## 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 $${\mathfrak{gl}}(n+1|n)$$.

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 Monday, January 21, 2019