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Some properties of distal actions on locally compact groups

Published online by Cambridge University Press:  07 September 2017

C. R. E. RAJA  and
RIDDHI SHAH
C. R. E. RAJA
Affiliation:
Stat-Math Unit, Indian Statistical Institute (ISI), 8th Mile, Mysore Road, Bangalore 560 059, India email [email protected]
RIDDHI SHAH
Affiliation:
School of Physical Sciences (SPS), Jawaharlal Nehru University (JNU), New Delhi 110 067, India email [email protected], [email protected]
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Abstract

We consider the actions of (semi)groups on a locally compact group by automorphisms. We show the equivalence of distality and pointwise distality for the actions of a certain class of groups. We obtain a decomposition for contraction groups of an automorphism under certain conditions. We give a necessary and sufficient condition for distality of an automorphism in terms of its contraction group. We compare classes of (pointwise) distal groups and groups whose closed subgroups are unimodular. In particular, we study relations between distality, unimodularity and contraction subgroups.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 5 , May 2019 , pp. 1340 - 1360
Copyright
© Cambridge University Press, 2017 

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