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arXiv · 2011.07339

Defining relations and Gr\"obner--Shirshov bases of Poisson algebras as of conformal modules

P. S. Kolesnikov·A. S. Panasenko
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Abstract

We study the relation between Poisson algebras and representations of Lie conformal algebras. We establish a setting for the calculation of a Gr\"obner--Shirshov basis in a module over an associative conformal algebra and apply this technique to Poisson algebras considered as conformal modules over appropriate associative envelopes of current Lie conformal algebras. As a result, we obtain a setting for the calculation of a Gr\"obner--Shirshov basis in a Poisson algebra.

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P. S. Kolesnikov, A. S. Panasenko. 2020-11-14. Defining relations and Gr\"obner--Shirshov bases of Poisson algebras as of conformal modules. https://doi.org/10.1142/s0219498822501389

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