Topological T-duality Via Lie Algebroids and Q-flux in Poisson-generalized Geometry

It is known that the topological T-duality exchanges H- and F-fluxes. In this paper, we reformulate the topological T-duality as an exchange of two Lie algebroids in the generalized tangent bundle. Then, we apply the same formulation to the Poisson-generalized geometry, which is introduced [T. Asakawa, H. Muraki, S. Sasa and S. Watamura, Int. J. Mod. Phys. A 30, 1550097 (2015), arXiv:1408.2649 [hep-th]] to define R-fluxes as field strength associated with [Formula: see text]-transformations. We propose a definition of Q-flux associated with [Formula: see text]-diffeomorphisms, and show that the topological T-duality exchanges R- and Q-fluxes.