Poisson double structures
arXiv:2106.15403 · doi:10.3934/jgm.2021029
Abstract
We introduce Poisson double algebroids, and the equivalent concept of double Lie bialgebroid, which arise as second-order infinitesimal counterparts of Poisson double groupoids. We develop their underlying Lie theory, showing how these objects are related by differentiation and integration. We use these results to revisit Lie 2-bialgebras by means of Poisson double structures.
arXiv comment28 pages. Dedicated to the memory of Kirill Mackenzie
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