T-duality and mirror symmetry on nilmanifolds : T-dualidade e simetria do espelho em nilvariedades

Abstract

We study a version of T-duality on nilmanifolds through a Lie theoretic point of view: we build the duality on the nilpotent Lie algebras and integrate it to corresponding nilmanifolds. This allows us to transport generalized complex structures between them using the tools developed by Cavalcanti and Gualtieri. In some cases, this transport exhibits a mirror symmetric behaviour. Inspired by homological mirror symmetry, we use this machinery to transport generalized complex branes between these T-dual pairs.