Revista Matemática Iberoamericana


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Published online first: 2019-12-17
DOI: 10.4171/rmi/1137

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

Roberto Rubio[1] and Carl Tipler[2]

(1) Weizmann Institute of Science, Rehovot, Israel and Universitat Autònoma de Barcelona, Spain
(2) Université de Bretagne Occidentale, Brest, France

We endow the group of automorphisms of an exact Courant algebroid over a compact manifold with an infinite dimensional Lie group structure modeled 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.

Keywords: Courant algebroid, generalized diffeomorphism, ILH Lie group, generalized metric

Rubio Roberto, Tipler Carl: The Lie group of automorphisms of a Courant algebroid and the moduli space of generalized metrics. Rev. Mat. Iberoam. Electronically published on December 17, 2019. doi: 10.4171/rmi/1137 (to appear in print)