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Description: |
In this talk, we state and prove most known results (established by Iglesias-Marrero and Grabowski-Marmo) about Jacobi algebroids and bialgebroids using the supergeometric formalism, more precisely, the so-called "big bracket", a formalism where brackets and anchors are encoded by functions on some graded symplectic manifold. Using these functions we describe the Jacobi Gerstenhaber algebra structure associated to a Jacobi algebroid and its Poissonization. Then, we express the compatibility condition defining Jacobi bialgebroids. In a second part, we re-explain how Jacobi structures give rise to Jacobi bialgebroids, i.e. how the functions encoding the Jacobi bialgebroid are constructed out of the sections defining the Jacobi structure.
Joint work with Camille Laurent-Gengoux.
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