Dirac geometry and integration of Poisson homogeneous spaces (Q6561312)

The paper investigates the integrability of Poisson homogeneous spaces from the viewpoint of Dirac geometry.\N\NThe authors show that any Poisson homogeneous space of a Poisson-Lie group is integrable,\Nand construct pre-symplectic groupoids explicitly for affine Dirac structures over Poisson-Lie groups.\N\NIt is well known that the concepts of Lie groupoids, Lie algebroids and the integrability of Lie algebroids can be generalized to the category of holomorphic manifolds. The results in Sections 2--6 prove to hold in the category of holomorphic Poisson manifolds as well.\NFor example, it is shown that any complex Poisson homogeneous space of a complex Poisson-Lie group is integrable.\NThe methods in the paper used for solving the integrability problem are based on the techniques in Dirac geometry\N(see [\textit{E. Meinrenken}, Lett. Math. Phys. 108, No. 3, 447--498 (2018; Zbl 1387.53107)], for instance).