Free lamplighter groups and a question of Atiyah
نویسندگان
چکیده
منابع مشابه
Free Lamplighter Groups and a Question of Atiyah
We compute the von Neumann dimensions of the kernels of adjacency operators on free lamplighter groups and show that they are irrational, thus providing an elementary constructive answer to a question of Atiyah.
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We prove that there are examples of finitely generated groups Γ together with group ring elements Q ∈ QΓ for which the von Neumann dimension dimLΓ kerQ is irrational, so (in conjunction with other known results) disproving a conjecture of Atiyah.
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We study automata groups generated by reset automata. Every lamplighter group Z/nZ wr Z can be generated by such an automaton, and in general these automata groups are similar in nature to lamplighters: they are amenable locally-finite-by-cyclic groups; under mild decidable conditions, the semigroups generated by such automata are free. Parabolic subgroups and fractal properties are considered.
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2013
ISSN: 1080-6377
DOI: 10.1353/ajm.2013.0029