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- W2157997896 abstract "We obtain sufficient and necessary conditions for the Choquet- Deny theorem to hold in the class of compactly generated totally disconnected locally compact groups of polynomial growth, and in a larger class of totally disconnected generalized FC -groups. The following conditions turn out to be equivalent when G is a metrizable compactly generated totally disconnected locally compact group of polynomial growth: (1) The Choquet-Deny theorem holds for G. (2) The group of inner automorphisms of G acts distally on G. (3) Every inner automorphism of G is distal. (4) The contraction subgroup of every inner automorphism of G is trivial. (5) G is a SIN group. We also show that for every probability measure μ on a totally disconnected compactly generated locally compact second countable group of polynomial growth, the Poisson boundary is a homogeneous space of G, and that it is a compact homogeneous space when the support of μ generates G." @default.
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- W2157997896 date "2007-02-14" @default.
- W2157997896 modified "2023-09-27" @default.
- W2157997896 title "The Choquet-Deny theorem and distal properties of totally disconnected locally compact groups of polynomial growth" @default.
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