Journal of Symplectic Geometry

Volume 17 (2019)

Number 1

Dirac groupoids and Dirac bialgebroids

Pages: 179 – 238



M. Jotz Lean (Mathematisches Institut, Georg-August Universität Göttingen, Germany)


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-2-forms, respectively. In the case of multiplicative involutive distributions on Lie groupoids, we find new properties of infinitesimal ideal systems.

Received 2 June 2015

Accepted 14 June 2018

Published 23 May 2019