The Lie group of automorphisms of a Courant algebroid and the moduli space of generalized metrics

TL;DR

This paper constructs an infinite-dimensional Lie group structure for automorphisms of Courant algebroids, analyzes their action on generalized metrics, and explores the resulting stratified moduli space, extending results to odd algebroids.

Contribution

It introduces an ILH Lie group structure on automorphisms of Courant algebroids and proves a slice theorem for their action on generalized metrics.

Findings

The automorphism group forms an ILH Lie group.

The moduli space of generalized metrics is stratified by ILH submanifolds.

Results extend to odd Courant algebroids.

Abstract

We endow the group of automorphisms of an exact Courant algebroid over a compact manifold with an infinite dimensional Lie group structure modelled on the inverse limit of Hilbert spaces (ILH). We prove a slice theorem for the action of this Lie group on the space of generalized metrics. As an application, we show that the moduli space of generalized metrics is stratified by ILH submanifolds and relate it to the moduli space of usual metrics. Finally, we extend these results to odd exact Courant algebroids.