We introduce the notion of Glanon groupoids, which are Lie groupoids equipped with multiplicative generalized complex structures. It combines symplectic groupoids, holomorphic Lie groupoids and holomorphic Poisson groupoids into a unified framework. Their infinitesimal, Glanon Lie algebroids are studied. We prove that there is a bijection between Glanon Lie algebroids and source-simply connected and source-connected Glanon groupoids. As a consequence, we recover various integration theorem and obtain the integration theorem for holomorphic Poisson groupoids.
Categories: math.DG math-ph math.MP