The group of autoequivalences of an exact Courant algebroid as a tame Fr\'echet Lie group

Abstract

The aim of this manuscript is to show that the group of autoequivalences of an exact Courant algebroid over a compact base manifold is a tame Fr\'echet Lie group. Moreover, we compute its Lie algebra. Furthermore, we show that the space of generalized almost complex structures is a tame Fr\'echet manifold and that the canonical action of the group of autoequivalences on the space of generalized almost complex structures is smooth tame.