Finite ergodic index and asymmetry for infinite measure preserving actions

Given k > 0 and an Abelian countable discrete group G with elements of infinite order, we construct (i) rigid funny rank-one infinite measure preserving (i.m.p.) G-actions of ergodic index k, (ii) 0-type funny rank-one i.m.p. G-actions of ergodic index k, (iii) funny rank-one i.m.p. G-actions T o...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2016-06, Vol.144 (6), p.2521-2532
Main Author: Danilenko, Alexandre I.
Format: Article
Language:English
Subjects:
B. ANALYSIS
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Summary:Given k > 0 and an Abelian countable discrete group G with elements of infinite order, we construct (i) rigid funny rank-one infinite measure preserving (i.m.p.) G-actions of ergodic index k, (ii) 0-type funny rank-one i.m.p. G-actions of ergodic index k, (iii) funny rank-one i.m.p. G-actions T of ergodic index 2 such that the product T × T −1 is not ergodic. It is shown that T × T −1 is conservative for each funny rank-one G-action T. 2010 Mathematics Subject Classification. Primary 37A40.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/12906