Recurrence in unipotent groups and ergodic nonabelian group extensions |
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Authors: | Gernot Greschonig |
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Institution: | 1.Faculty of Mathematics,University of Vienna,Vienna,Austria |
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Abstract: | LetT be a measure-preserving and ergodic transformation of a standard probability space (X,S, μ) and letf:X → SUT
d
(ℝ) be a Borel map into the group of unipotent upper triangulard ×d matrices. We modify an argument in 12] to obtain a sufficient condition for the recurrence of the random walk defined byf, in terms of the asymptotic behaviour of the distributions of the suitably scaled mapsf(n,x)=(fT
n−1·fT
n−2…fT·f). We give examples of recurrent cocycles with values in the continuous Heisenberg group H1(ℝ)=SUT3(ℝ), and we use a recurrent cocycle to construct an ergodic skew-product extension of an irrational rotation by the discrete
Heisenberg group H1(ℤ)=SUT3(ℤ).
The author was partially supported by the FWF research project P16004-MAT. |
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Keywords: | |
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