Dualit\'e de Van den Bergh et Structure de Batalin-Vilkovisky sur les alg\`ebres de Calabi-Yau

TL;DR

This paper demonstrates that Calabi-Yau algebras inherently possess Batalin-Vilkovisky (BV) algebra structures by applying the Tamarkin-Tsygan calculus with duality to Van den Bergh duality.

Contribution

It introduces a novel application of Tamarkin-Tsygan calculus with duality to establish BV structures on Calabi-Yau algebras, expanding the understanding of their algebraic properties.

Findings

Calabi-Yau algebras are BV-algebras

Application of Tamarkin-Tsygan calculus with duality

Generalization of BV structures in algebraic geometry

Abstract

The abstract notion of Tamarkin-Tsygan calculus with duality gives Batalin- Vilkovisky structures in a general setting. We apply this technique to the case of Van den Bergh duality for algebras to prove that Calabi-Yau algebras are BV-algebras.