Jacobi algebroids and quasi Q-manifolds

TL;DR

This paper introduces a reformulation of Jacobi algebroids using weighted odd Jacobi brackets and connects them to curved Q-manifolds, leading to the concept of quasi Q-manifolds with deformed homological conditions.

Contribution

It provides a new formulation of Jacobi algebroids via weighted odd Jacobi brackets and introduces quasi Q-manifolds with deformed homological conditions.

Findings

Reformulation of Jacobi algebroids using weighted odd Jacobi brackets

Introduction of quasi Q-manifolds with deformed homological conditions

Establishment of a connection between Jacobi algebroids and curved Q-manifolds

Abstract

We reformulate the notion of a Jacobi algebroid in terms of weighted odd Jacobi brackets. We then show how a Jacobi algebroid can be understood in terms of a kind of curved Q-manifold. In particular the homological condition on the odd vector field is deformed in a very specific way. This leads to the notion of a quasi Q-manifold.