We study the relation between Poisson algebras and representations of Lie conformal algebras. We establish a Gröbner–Shirshov basis theory framework for modules over associative conformal algebras and apply this technique to Poisson algebras considered as conformal modules over appropriate associative conformal envelopes of current Lie conformal algebras. As a result, we obtain a setting for the calculation of a Gröbner–Shirshov basis in a Poisson algebra.

中文翻译：

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将泊松代数的关系和 Gröbner-Shirshov 基定义为保形模

我们研究了泊松代数与李共形代数表示之间的关系。我们为关联共形代数上的模块建立了 Gröbner-Shirshov 基础理论框架，并将该技术应用于泊松代数，被认为是当前李共形代数的适当关联共形包络上的共形模块。结果，我们获得了用于计算泊松代数中的 Gröbner-Shirshov 基的设置。