Extend the tame Lie-group structure to general transitive Courant algebroids

Establish that the groups of all autoequivalences and exact autoequivalences of every transitive Courant algebroid form tame Fréchet Lie groups, with the exact autoequivalences forming a tame Lie subgroup whose action on sections is by inner derivations, in order to support an extension of Gualtieri’s locally complete deformation theorem from mathcal{G}-flat transitive Courant algebroids to arbitrary transitive Courant algebroids.

Background

The paper proves a deformation theorem for generalized complex structures on mathcal{G}-flat transitive Courant algebroids. A key analytic ingredient is the construction of tame Fréchet Lie-group structures on the full group of Courant autoequivalences and on the subgroup of exact autoequivalences; the latter has infinitesimal action given by inner derivations. The deformation argument also relies on the associated Lie algebroid complex being elliptic and on the smooth tame action of these groups on generalized complex structures.

The authors state that the core of their proof does not depend on the explicit formulas special to the mathcal{G}-flat case, but only on the ellipticity of the Lie algebroid complex and the relevant tame Lie-group and action properties. They therefore conjecture that these structural properties persist for arbitrary transitive Courant algebroids. Proving this would provide the foundation for extending the locally complete-family result to the full transitive setting.