On the singularities of the exponential function of a semidirect product

Abstract

We show that the Fréchet--Lie groups of the form $C^{\infty }(M)⋊\mathbb{R}$ resulting from smooth flows on compact manifolds $M$ fail to be locally exponential in several cases: when at least one non-periodic orbit is locally closed, or when the flow restricts to a linear one on an orbit closure diffeomorphic to a torus. As an application, we prove that the Bondi--Metzner--Sachs group of symmetries of an asymptotically flat spacetime is not locally exponential.

26 pages + references; v4: accepted version, to appear in Classical and Quantum Gravity

References in corpus (1)

• Lie Theory for Asymptotic Symmetries in General Relativity: The BMS Group

Cited by in corpus (1)

• Group Contractions via Infinite-Dimensional Lie Theory