Bernoulli measure on strings, and Thompson-Higman monoids
نویسندگان
چکیده
منابع مشابه
Coherent Presentations of Structure Monoids and the Higman-thompson Groups
Structure monoids and groups are algebraic invariants of equational varieties. We show how to construct presentations of these objects from coherent categorifications of equational varieties, generalising several results of Dehornoy. We subsequently realise the higher Thompson groups Fn,1 and the Higman-Thompson groups Gn,1 as structure groups. We go on to obtain presentations of these groups v...
متن کاملThe homology of the Higman–Thompson groups
We prove that Thompson’s group V is acyclic, answering a 1992 question of Brown in the positive. More generally, we identify the homology of the Higman–Thompson groups Vn,r with the homology of the zeroth component of the infinite loop space of the mod n− 1 Moore spectrum. As V = V2,1, we can deduce that this group is acyclic. Our proof involves establishing homological stability with respect t...
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We prove that the only finite factor-representations of the HigmanThompson groups {Fn,r}, {Gn,r} are the regular representations and scalar representations arising from group abelianizations. As a corollary, we obtain that any measure-preserving ergodic action of a simple Higman-Thompson group must be essentially free. Finite factor representations of other classes of groups are also discussed.
متن کاملFactorizations of the Thompson-higman Groups, and Circuit Complexity
We consider the subgroup lpGk,1 of length preserving elements of the Thompson-Higman group Gk,1 and we show that all elements of Gk,1 have a unique lpGk,1 · Fk,1 factorization. This applies to the Thompson-Higman group Tk,1 as well. We show that lpGk,1 is a “diagonal” direct limit of finite symmetric groups, and that lpTk,1 is a k ∞ Prüfer group. We find an infinite generating set of lpGk,1 whi...
متن کاملTamari lattices, forests and Thompson monoids
A connection relating Tamari lattices on symmetric groups regarded as lattices under the weak Bruhat order to the positive monoid P of Thompson group F is presented. Tamari congruence classes correspond to classes of equivalent elements in P. The two well known normal forms in P correspond to endpoints of intervals in the weak Bruhat order that determine the Tamari classes. In the monoid P thes...
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ژورنال
عنوان ژورنال: Semigroup Forum
سال: 2011
ISSN: 0037-1912,1432-2137
DOI: 10.1007/s00233-011-9302-1