English

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-22-forms, respectively. In the case of multiplicative involutive distributions on Lie groupoids, we find new properties of infinitesimal ideal systems.

Keywords

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

R2 v1 2026-06-22T03:25:09.877Z