Differential Gerstenhaber algebras of generalized complex structures (Q407350)

This paper identifies the infinitesimal conditions of differential Gerstenhaber algebras as the deformations of generalized complex structures. Let us recall that a differential Gerstenhaber algebra (DGA) is associated to every generalized complex structure. In this work, the authors prove that the infinitesimal conditions are always integrable. For nilmanifolds, that is compact quotients of simply connected nilpotent Lie groups, it is proved that the invariant DGA is quasi-isomorphic to the full DGA of the symplectic structure. A general construction to solve the infinitesimal conditions is obtained. The existence of the solutions is also studied in detail.