Abstract
This paper is the first part of a dilogy devoted to modular classes of Jacobi structures from the general line bundle perspective as well as their associated Lie algebroids. First, we explain the relationship between Jacobi algebroids and their associated Gerstenhaber-Jacobi algebras. Then, we show that given a Jacobi manifold, there is a differential complex associated to it whose differential operator is similar to the so-called Koszul-Brylinski operator. This allows us to define Jacobi homology for Jacobi bundles. Moreover, we show that there are generating operators for the Gerstenhaber-Jacobi algebra associated to the Atiyah algebroid DL whose sections are derivations of the associated line bundle L.
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Acknowledgements
Mamadou Lamarana Diallo was partially supported by the NLAGA project funded by Simons Foundation. The authors would like to thank Luca Vitagliano for useful suggestions during the preparation of this manuscript and the anonymous referee for her/his comments.
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Communicated by Claudio Gorodski.
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Diallo, M.L., Wade, A. Modular classes of Jacobi bundles. São Paulo J. Math. Sci. 15, 505–523 (2021). https://doi.org/10.1007/s40863-021-00227-2
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DOI: https://doi.org/10.1007/s40863-021-00227-2