Odd Jacobi manifolds: general theory and applications to generalised Lie algebroids

Abstract

In this paper we define a Grassmann odd analogue of Jacobi structure on a supermanifold. The basic properties are explored. The construction of odd Jacobi manifolds is then used to reexamine the notion of a Jacobi algebroid. It is shown that Jacobi algebroids can be understood in terms of a kind of curved Q-manifold, which we will refer to as a quasi Q-manifold.

35 pages. This preprint is an amalgamation of the earlier preprints arXiv:111.4044, arXiv:1103.1803 and arXiv:1101.1844. A version of this work appears in Extracta Mathematicae

References in corpus (2)

• $Q$-manifolds and Higher Analogs of Lie Algebroids
• Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic Mechanics