Geodesic
On irreducibility of Koopman representations corresponding to measure contracting actions
Artem Dudko1
1Polish Academy of Sciences, Warsaw, Poland
Groups, geometry, and dynamics, Tome 12 (2018) no. 4, pp. 1417-1427

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DOI

We introduce a notion of measure contracting actions and show that Koopman representations corresponding to ergodic measure contracting actions are irreducible. We also show that the actions of Higman–Thompson groups on intervals equipped with Lebesgue measure and the actions of weakly branch groups on the boundaries of rooted trees equipped with non-uniform Bernoulli measures are measure contracting. This gives a new point of view on irreducibility of the corresponding Koopman representations.
DOI : 10.4171/ggd/473
Classification : 37-XX, 20-XX
Mots-clés : Koopman representation, irreducibility, measure contracting actions, Higman–Thompson groups, weakly branch groups

Artem Dudko  1

1 Polish Academy of Sciences, Warsaw, Poland 
Artem Dudko. On irreducibility of Koopman representations corresponding to measure contracting actions. Groups, geometry, and dynamics, Tome 12 (2018) no. 4, pp. 1417-1427. doi: 10.4171/ggd/473
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     title = {On irreducibility of {Koopman} representations corresponding to measure contracting actions},
     journal = {Groups, geometry, and dynamics},
     pages = {1417--1427},
     year = {2018},
     volume = {12},
     number = {4},
     doi = {10.4171/ggd/473},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/473/}
}
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