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

  title={On a Batalin–Vilkovisky operator generating higher Koszul brackets on differential forms},
  author={Ekaterina Shemyakova},
  journal={Letters in Mathematical Physics},
  • 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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