# On a Batalin–Vilkovisky operator generating higher Koszul brackets on differential forms

@article{Shemyakova2021OnAB,
title={On a Batalin–Vilkovisky operator generating higher Koszul brackets on differential forms},
author={Ekaterina Shemyakova},
journal={Letters in Mathematical Physics},
year={2021},
volume={111},
pages={1-30}
}
• E. Shemyakova
• Published 30 March 2021
• Mathematics
• Letters in Mathematical Physics
We introduce a formal $$\hbar$$ -differential operator $$\Delta$$ that generates higher Koszul brackets on the algebra of (pseudo)differential forms on a $$P_{\infty }$$ -manifold. Such an operator was first mentioned by Khudaverdian and Voronov in arXiv:1808.10049. (This operator is an analogue of the Koszul–Brylinski boundary operator $$\partial _P$$ which defines Poisson homology for an ordinary Poisson structure.) Here, we introduce $$\Delta =\Delta _P$$ by a different method and…
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