Some properties of distal actions on locally compact groups
Copyright policy )Some properties of distal actions on locally compact groups
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.
Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.), automorphisms, Actions of groups and semigroups; invariant theory (associative rings and algebras), distality, contraction subgroups, Dynamical Systems (math.DS), Group Theory (math.GR), 37B05, 22D05 (Primary), 22E15, 22D45 (Secondary), General theory of group and pseudogroup actions, unimodularity, FOS: Mathematics, locally compact group, Mathematics - Dynamical Systems, Mathematics - Group Theory
Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.), automorphisms, Actions of groups and semigroups; invariant theory (associative rings and algebras), distality, contraction subgroups, Dynamical Systems (math.DS), Group Theory (math.GR), 37B05, 22D05 (Primary), 22E15, 22D45 (Secondary), General theory of group and pseudogroup actions, unimodularity, FOS: Mathematics, locally compact group, Mathematics - Dynamical Systems, Mathematics - Group Theory
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