# 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} }

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…

## 4 Citations

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## References

SHOWING 1-10 OF 52 REFERENCES

Thick morphisms, higher Koszul brackets, and $L_{\infty}$-algebroids

- Mathematics
- 2018

It is a classical fact in Poisson geometry that the cotangent bundle of a Poisson manifold has the structure of a Lie algebroid. Manifestations of this structure are the Lichnerowicz differential on…

On odd Laplace operators. II

- Mathematics
- 2002

We analyze geometry of the second order differential operators, having in mind applications to Batalin--Vilkovisky formalism in quantum field theory. As we show, an exhaustive picture can be obtained…

The BV formalism for $$L_\infty $$L∞-algebras

- Mathematics
- 2017

Functorial properties of the correspondence between commutative $${{\mathrm{BV}}}_\infty $$BV∞-algebras and $$L_\infty $$L∞-algebras are investigated. The category of $$L_\infty $$L∞-algebras with…

NONCOMMUTATIVE DIFFERENTIAL CALCULUS

- Mathematics
- 2015

This is a note from B. Tsygan’s lecture series which was part of masterclass “Algebraic structure of Hochschild complexes” at the University of Copenhagen in October 2015. From the course…

Differential forms and odd symplectic geometry

- Mathematics
- 2006

We recall the main facts about the odd Laplacian acting on half-densities on an odd symplectic manifold and discuss a homological interpretation for it suggested recently by P. {\v{S}}evera. We study…

Differential operators on the algebra of densities and factorization of the generalized Sturm–Liouville operator

- MathematicsLetters in Mathematical Physics
- 2018

We consider factorization problem for differential operators on the commutative algebra of densities (defined either algebraically or in terms of an auxiliary extended manifold) introduced in 2004 by…

Derived Brackets

- Mathematics
- 2004

We survey the many instances of derived bracket construction in differential geometry, Lie algebroid and Courant algebroid theories, and their properties. We recall and compare the constructions of…

Graded Manifolds and Drinfeld Doubles for Lie Bialgebroids

- Mathematics
- 2001

We define graded manifolds as a version of supermanifolds endowed with an extra Z-grading in the structure sheaf, called weight (not linked
with parity). Examples are ordinary supermanifolds, vector…

Q-Manifolds and Mackenzie Theory

- Mathematics
- 2012

Double Lie algebroids were discovered by Kirill Mackenzie from the study of double Lie groupoids and were defined in terms of rather complicated conditions making use of duality theory for Lie…