Generalized Jacobi structures

TL;DR

This paper introduces a new class of brackets extending Jacobi structures to multiple functions, encompassing generalized Poisson structures, with applications to simple group manifolds and novel examples derived from cohomology.

Contribution

It generalizes Jacobi brackets to involve multiple functions and explores their properties and examples, including on simple group manifolds.

Findings

Includes generalized Poisson structures as a special case

Provides non-trivial examples from cohomology rings

Studies linear cases on simple group manifolds

Abstract

Jacobi brackets (a generalization of standard Poisson brackets in which Leibniz's rule is replaced by a weaker condition) are extended to brackets involving an arbitrary (even) number of functions. This new structure includes, as a particular case, the recently introduced generalized Poisson structures. The linear case on simple group manifolds is also studied and non-trivial examples (different from those coming from generalized Poisson structures) of this new construction are found by using the cohomology ring of the given group.