Actions of automorphism groups of Lie groups

Abstract

This is an expository article on properties of actions on Lie groups by subgroups of their automorphism groups. After recalling various results on the structure of the automorphism groups, we discuss actions with dense orbits, invariant and quasi-invariant measures, the induced actions on the spaces of probability measures on the groups, and results concerning various issues in ergodic theory, topological dynamics, smooth dynamical systems, and probability theory on Lie groups.

39 pages; to appear in the Handbook of Group Actions, (ed. L. Ji, A. Papadopoulos and S.-T. Yau), Volume IV, International Press and Higher Education Press, 2017

Cited by in corpus (1)

• Expansive Actions of Automorphisms of Locally Compact Groups $G$ on ${\mathrm{Sub}}_G$