Dirac groupoids and Dirac bialgebroids

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.

Full Text (PDF format)

Received 2 June 2015

Accepted 14 June 2018

Published 23 May 2019