August 17, 2025Open Access

Batalin-Vilkovisky structures on the cohomologies of tensor Poisson algebras

Key Points

The tensor algebra of two pseudo-unimodular Poisson algebras retains a Batalin-Vilkovisky algebra structure, ensuring theoretical consistency.
Batalin-Vilkovisky algebra of the tensor algebra is shown to be isomorphic to the combined structures of individual Poisson cohomology rings.
This research highlights the importance of pseudo-unimodularity in establishing algebraic properties between tensor algebra.
The findings contribute to the broader understanding of Poisson algebra structures and their cohomological implications.

Abstract

It has been proved that the Poisson cohomology ring of a Poisson algebra has a Batalin-Vilkovisky algebra structure iff the Poisson algebra is pseudo-unimodular. In this paper, it is proved that the tensor algebra of two pseudo-unimodular Poisson algebras is also pseudo-unimodular, thus its Poisson cohomology ring is still a Batalin-Vilkovisky algebra. Furthermore, This Batalin-Vilkovisky algebra is isomorphic to the tensor Batalin-Vilkovisky algebra of the respective Poisson cohomology rings of the two pseudo-unimodular Poisson algebras.

Read Full Paperexternally

Bookmark

View Full Paper

Cite This Study

Luo et al. (Wed,) studied this question.

synapsesocial.com/papers/68a36dd20a429f7973330be4 https://doi.org/https://doi.org/10.2298/fil2509913l

Bookmark

View Full Paper