On generalized Lie bialgebroids and Jacobi groupoids

Abstract

Generalized Lie bialgebroids are generalization of Lie bialgebroids and arises naturally from Jacobi manifolds. It is known that the base of a generalized Lie bialgebroid carries a Jacobi structure. In this paper, we introduce a notion of morphism between generalized Lie bialgebroids over a same base and prove that the induce Jacobi structure on the base is unique up to a morphism. Next we give a characterization of generalized Lie bialgebroids and use it to show that generalized Lie bialgebroids are infinitesimal form of Jacobi groupoids. We also introduce coisotropic subgroupoids of a Jacobi groupoid and these subgroupoids corresponds to, so called coisotropic subalgebroids of the corresponding generalized Lie bialgebroid.