T-duality on nilmanifolds

Abstract

We study generalized complex structures and T-duality (in the sense of Bouwknegt, Evslin, Hannabuss and Mathai) on Lie algebras and construct the corresponding Cavalcanti and Gualtieri map. Such a construction is called Infinitesimal T -duality. As an application we deal with the problem of finding symplectic structures on 2-step nilpotent Lie algebras. We also give a criteria for the integrability of the infinitesimal T-duality of Lie algebras to topological T-duality of the associated nilmanifolds.