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

Bruce, Andrew James

Extr. Math. 27, No. 1, 91-123 (2012).

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

Keywords:

supermanifolds; Jacobi structures; Lie algebroids