On compact group extension of Bernoulli shifts

Z Group Shifts and Bernoulli Factors

In this paper, a group shift is an expansive action of Zd on a compact metrizable zero dimensional group by continuous automorphisms. All group shifts factor topologically onto equal-entropy Bernoulli shifts; abelian group shifts factor by continuous group homomorphisms onto canonical equalentropy Bernoulli group shifts; and completely positive entropy abelian group shifts are weakly algebraica...

galois extension for a compact quantum group

The aim of this paper is to introduce the quantum analogues of torsors for a compact quantum group and to investigate their relations with representation theory. Let A be a Hopf algebra over a field k. A theorem of Ulbrich asserts that there is an equivalence of categories between neutral fibre functors on the category of finitedimensional A-comodules and A-Galois extensions of k. We give the c...

Weak isomorphisms between Bernoulli shifts

In this note, we prove that if G is a countable group that contains a nonabelian free subgroup then every pair of nontrivial Bernoulli shifts over G are weakly isomorphic.

Brooks’ theorem for Bernoulli shifts

If Γ is an infinite group with finite symmetric generating set S, we consider the graph G(Γ, S) on [0, 1]Γ by relating two distinct points if an element of s sends one to the other via the shift action. We show that, aside from the cases Γ = Z and Γ = (Z/2Z) ∗ (Z/2Z), G(Γ, S) satisfies a measure-theoretic version of Brooks’ theorem: there is a G(Γ, S)-invariant conull Borel set B ⊆ [0, 1]Γ and ...

Institute for Mathematical Physics Resolving Markov Chains onto Bernoulli Shifts Resolving Markov Chains onto Bernoulli Shifts