paper

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.

28 pages. Dedicated to the memory of Kirill Mackenzie