Jacobi structures in supergeometric formalism

We use the supergeometric formalism, more precisely, the so-called “big bracket” (for which brackets and anchors are encoded by functions on some graded symplectic manifold) to address the theory of Jacobi algebroids and bialgebroids, following mainly the previous works of Iglesias–Marrero [9] and Grabowski–Marmo [10]. This formalism is efficient to define the Jacobi–Gerstenhaber algebra structure associated to a Jacobi algebroid, to define its Poissonization, and to express the compatibility condition defining Jacobi bialgebroids. It also yields a simple description of the Jacobi bialgebroid associated to a Jacobi structure, and conversely, of the Jacobi structure associated to a Jacobi bialgebroid.

► We use supergeometric formalism to address the theory of Jacobi (bi-)algebroids. ► We give a characterization of Jacobi bialgebroid structures. ► Let (π,E)(π,E) be a Jacobi structure on a Lie algebroid μμ. ► The Poissonization of ν−Eν−E on AA is the Lie algebroid associated with the Poissonization of (π,E)(π,E).