S.G. Dani, Tata Institute

Locally compact groups with ergodic Z^n-actions by automorphisms

Wednesday February 22, 4:00PM, Herman Brown 227
In his book on ergodic theory P.R. Halmos had asked the question whether a noncompact locally compact group can admit an automorphism which is ergodic, with respect to the Haar measure. The answer has been known to be in the negative. However, for n≥2 a locally compact group on which there is an ergodic Z^n-action by automorphisms does not have to be compact. In particular it can be seen that any locally compact field of characteristic zero (viewed as a group under addition) admits such actions. We consider general locally compact groups admitting such actions, and relate them to these examples.