Multiplicative Dirac structures on Lie groups

TL;DR

This paper investigates multiplicative Dirac structures on Lie groups, revealing their foliation by normal Lie subgroup cosets and conditions under which the leaf space forms a Poisson-Lie group, along with their infinitesimal descriptions.

Contribution

It characterizes the foliation and leaf space structure of multiplicative Dirac structures on Lie groups and provides their infinitesimal descriptions, advancing understanding of their geometric properties.

Findings

Characteristic foliation given by cosets of a normal Lie subgroup

Leaf space inherits a Poisson-Lie group structure when subgroup is closed

Infinitesimal description of multiplicative Dirac structures

Abstract

We study multiplicative Dirac structures on Lie groups. We show that the characteristic foliation of a multiplicative Dirac structure is given by the cosets of a normal Lie subgroup and, whenever this subgroup is closed, the leaf space inherits the structure of a Poisson-Lie group. We also describe multiplicative Dirac structures on Lie groups infinitesimally.