Dirac groupoids and Dirac bialgebroids
Differential Geometry
2015-05-29 v2
Abstract
We describe infinitesimally Dirac groupoids via geometric objects that we call Dirac bialgebroids. In the two well-understood special cases of Poisson and presymplectic groupoids, the Dirac bialgebroids are equivalent to the Lie bialgebroids and IM--forms, respectively. In the case of multiplicative involutive distributions on Lie groupoids, we find new properties of infinitesimal ideal systems.
Cite
@article{arxiv.1403.2934,
title = {Dirac groupoids and Dirac bialgebroids},
author = {Madeleine Jotz Lean},
journal= {arXiv preprint arXiv:1403.2934},
year = {2015}
}
Comments
New expanded version; the construction of the Manin pair associated to an LA-Dirac structure has moved from arXiv:1209.6077 to here. Added background on double vector bundles, VB-algebroids and 2-term representations up to homotopy