We translate the construction of the chiral operad by Beilinson and Drinfeld to the purely algebraic language of vertex algebras. Consequently, the general construction of a cohomology complex associated to a linear operad produces the vertex algebra cohomology complex. Likewise, the associated graded of the chiral operad leads to the classical operad, which produces a Poisson vertex algebra cohomology complex. The latter is closely related to the variational Poisson cohomology studied by two of the authors.

中文翻译：

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顶点代数和泊松顶点代数上同调的操作方法

我们将 Beilinson 和 Drinfeld 的手性运算构造转化为顶点代数的纯代数语言。因此，与线性运算相关的上同调复形的一般构造产生顶点代数上同调复形。同样，手征运算的相关分级导致经典运算，产生泊松顶点代数上同调复形。后者与两位作者研究的变分泊松上同调密切相关。