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We study dg-manifolds which are R[2]-bundles over R[1]-bundles overmanifolds, we calculate its symmetries, its derived symmetries and we introducethe concept of T-dual dg-manifolds. Within this framework we construct theT-duality map as a degree -1 map between the cohomologies of the T-dualdg-manifolds and we show an explicit isomorphism between the differentialgraded algebra of the symmetries of the T-dual dg-manifolds. We furthermoreshow how the algebraic structure underlying B_n generalized geometry could berecovered as derived dg-Leibniz algebra of the fixed points of the T-dualautomorphism acting on the symmetries of a self T-dual dg-manifold, and we showhow other types of algebraic structures underlying exceptional generalizedgeometry could be obtained as derived symmetries of certain dg-manifolds.

T-duality and exceptional generalized geometry through symmetries of dg-manifolds