@inproceedings{c47346c24f0d4c70bb133a82ca1eb4b7,

title = "The Polycyclic Inverse Monoids and the Thompson Groups Revisited",

abstract = "We revisit our construction of the Thompson groups from the polycyclic inverse monoids in the light of new research. Specifically, we prove that the Thompson group Gn1 is the group of units of a Boolean inverse monoid Cn called the Cuntz inverse monoid. This inverse monoid is proved to be the tight completion of the polycyclic inverse monoid Pn. The {\'e}tale topological groupoid associated with Cn under non-commutative stone duality is the usual groupoid associated with the corresponding Cuntz C∗ -algebra. We then show that the group Gn 1 is also the group of automorphisms of a specific n-ary Cantor algebra: this n-ary Cantor algebra is constructed first as the monoid of total maps of a restriction semigroup {\`a} la Statman and then in terms of labelled trees {\`a} la Higman.",

keywords = "Cantor algebras, Free monoids, Polycyclic inverse monoids, Thompson groups, {\'e}tale groupoids",

author = "Lawson, {Mark V.}",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.; International Conference on Semigroups and Applications 2019, ICSAA 2019 ; Conference date: 09-12-2019 Through 12-12-2019",

year = "2021",

month = mar,

day = "27",

doi = "10.1007/978-981-33-4842-4_12",

language = "English",

isbn = "9789813348417",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "179--214",

editor = "Romeo, {P. G.} and Volkov, {Mikhail V.} and Rajan, {A. R.}",

booktitle = "Semigroups, Categories, and Partial Algebras. ICSAA 2019",

}