Deformations of generalized complex structures on $\mathcal{G}$-flat transitive Courant algebroids

Abstract

We extend Gualtieri's deformation theorem for generalized complex structures on exact Courant algebroids to the more general class of $\mathcal{G}$-flat transitive Courant algebroids. Our approach relies on the framework of tame Fr\'echet spaces and Hamilton's Nash-Moser (implicit function) theorem. As an important step of the proof of our deformation theorem, we endow the group of autoequivalences of a $\mathcal{G}$-flat transitive Courant algebroid with a tame Fr\'echet Lie group structure and show that there exists a tame subgroup of exact autoequivalences, whose infinitesimal action is by inner derivations.