# On higher Poisson and Koszul--Schouten brackets

## TL;DR

This paper demonstrates how to construct a homotopy BV-algebra on differential forms over a higher Poisson manifold using the Lie derivative as the generating operator.

## Contribution

It introduces a method to build a homotopy BV-algebra structure on differential forms in the context of higher Poisson geometry, utilizing the Lie derivative.

## Key findings

- Homotopy BV-algebra structure constructed on differential forms
- Lie derivative acts as the generating operator
- Extension of Poisson geometry to higher structures

## Abstract

In this note we show how to construct a homotopy BV-algebra on the algebra of differential forms over a higher Poisson manifold. The Lie derivative along the higher Poisson structure provides the generating operator.