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arXiv · 1012.2739

Jacobi structures in supergeometric formalism

Paulo dos Santos Antunes·Camille Laurent-Gengoux
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Abstract

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.

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Paulo dos Santos Antunes, Camille Laurent-Gengoux. 2010-12-13. Jacobi structures in supergeometric formalism. https://arxiv.org/abs/1012.2739

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