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

中文翻译：

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超对称 W-代数

我们在超对称顶点代数的背景下解释了 W 代数的一般理论。我们根据自由生成集来描述与李超代数奇幂零元相关的 W 代数的结构。作为一个应用，我们产生了与李超代数 $$\mathfrak {gl}(n+1|n)$$ gl ( n + 1 | n ) 的奇主幂零元相关联的 W -代数的显式自由生成器。