Generating Operators of the Krasil'shchik-Schouten bracket

TL;DR

This paper demonstrates how divergence operators on supermanifold sheaves can generate operators for the Krasil'shchik-Schouten bracket, extending to bigraded Gerstenhaber and $n$-graded Jacobi algebras.

Contribution

It introduces a method to construct generating operators for the Krasil'shchik-Schouten bracket using divergence operators, expanding the theory to bigraded Gerstenhaber and $n$-graded Jacobi algebras.

Findings

Constructed generating operators from divergence operators.

Extended the framework to bigraded Gerstenhaber algebras.

Discussed potential generalizations to $n$-graded Jacobi algebras.

Abstract

It is proved that given a divergence operator on the structural sheaf of graded commutative algebras of a supermanifold, it is possible to construct a generating operator for the Krashil'shchik-Schouten bracket. This is a particular case of the construction of generating operators for a special class of bigraded Gerstenhaber algebras. Also, some comments on the generalization of these results to the context of $n-$graded Jacobi algebras are included.