Dirac groupoids and Dirac bialgebroids

2014/03/12 by Lean, Madeleine Jotz
#53D17 #Differential Geometry (math.DG) #FOS: Mathematics #Primary: 58H05 #secondary: 70G45

paper · doi:10.48550/arxiv.1403.2934

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

Related

• Infinitesimal objects associated to Dirac groupoids and their homogeneous spaces
• Dirac structures and Poisson homogeneous spaces
• Multiplicative forms at the infinitesimal level
• Symmetries and reduction of multiplicative 2-forms
• Jacobi groupoids and generalized Lie bialgebroids