Lamplighter groups and von Neumann‘s continuous regular ring
نویسندگان
چکیده
منابع مشابه
Cross-wired lamplighter groups
We give a necessary and sufficient condition for a locally compact group to be isomorphic to a closed cocompact subgroup in the isometry group of a Diestel–Leader graph. As a consequence of this condition, we see that every cocompact lattice in the isometry group of a Diestel–Leader graph admits a transitive, proper action on some other Diestel–Leader graph. We also give some examples of lattic...
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Let (G, μ) be a discrete group with a generating probability measure. Nevo shows that if G has property (T) then there exists an ε > 0 such that the Furstenberg entropy of any (G, μ)-stationary space is either zero or larger than ε. Virtually free groups, such as SL2(Z), do not have property (T). For these groups, we construct stationary actions with arbitrarily small, positive entropy. This co...
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We consider the two generalizations of lamplighter groups: automata groups generated by Cayley machines and cross-wired lamplighter groups. For a finite step two nilpotent group with central squares, we study its associated Cayley machine and give a presentation of the corresponding automata group. We show the automata group is a crosswired lamplighter group and does not embed in the wreath pro...
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We compute the Bieri-Neumann-Strebel-Renz geometric invariants, Σn, of the lamplighter groups Lm by using the Diestel-Leader graph DL(m,m) to represent the Cayley graph of Lm.
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We calculate the spectra and spectral measures associated to random walks on restricted wreath products G wr Z, with G a finite abelian group, by realizing them as groups generated by automata. This generalizes the work of Grigorchuk and Żuk on the lamplighter group. More generally we calculate the spectra of random walks on groups generated by Cayley machines of finite groups and calculate Kes...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2016
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13066