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Odd Jacobi manifolds: general theory and applications to generalised Lie algebroids. (English) Zbl 1267.53086

Summary: 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.

MSC:

53D17 Poisson manifolds; Poisson groupoids and algebroids
53D10 Contact manifolds (general theory)
17B70 Graded Lie (super)algebras
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