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 Jacobi structures in supergeometric formalism

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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 Iglesias-Marrero and Grabowski-Marmo as a guideline. This formalism is in particular 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. Also, we claim that this supergeometric language gives a simple description of the Jacobi bialgebroid associated to Jacobi structures, and conversely, of the Jacobi structure associated to Jacobi bialgebroid.

Author: Paulo dos Santos Antunes; Camille Laurent-Gengoux

Source: https://archive.org/

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