95 research outputs found
Presentations of Topological Full Groups by Generators and Relations
We describe generators and defining relations for the commutator subgroup of
topological full groups of minimal subshifts. We show that the word problem in
a topological full group is solvable if and only if the language of the
underlying subshift is recursive.Comment: Some typos fixe
On irreducibility and disjointness of Koopman and quasi-regular representations of weakly branch groups
We study Koopman and quasi-regular representations corresponding to the
action of arbitrary weakly branch group G on the boundary of a rooted tree T.
One of the main results is that in the case of a quasi-invariant Bernoulli
measure on the boundary of T the corresponding Koopman representation of G is
irreducible (under some general conditions). We also show that quasi-regular
representations of G corresponding to different orbits and Koopman
representations corresponding to different Bernoulli measures on the boundary
of T are pairwise disjoint. This gives two continual collections of pairwise
disjoint irreducible representations of a weakly branch group. Another
corollary of our results is triviality of the centralizer of G in various
groups of transformations on the boundary of T
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