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Article Dans Une Revue Journal of Geometry and Physics Année : 2015

Jacobi structures in supergeometric formalism

Résumé

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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hal-01096575 , version 1 (21-02-2016)

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Paulo Antunes, Camille Laurent-Gengoux. Jacobi structures in supergeometric formalism. Journal of Geometry and Physics, 2015, 61 (11), pp.2254-2266. ⟨hal-01096575⟩
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