论文标题
多环逆的单体和汤普森组重新审视
The polycyclic inverse monoids and the Thompson groups revisited
论文作者
论文摘要
根据新的研究，我们重新审视了多环逆的汤普森组的构建。具体来说，我们证明了汤普森组$ g_ {n，1} $是布尔逆的单位单位组的组，称为cuntz倒数。事实证明，这种逆的单体被证明是多环的紧密完成。与$ c_ {n} $相关的étale拓扑群体在非交通型石头双重性下是与相应的cuntz $ c^{\ ast} $ - 代数相关的通常的groupoid。然后，我们表明该组$ g_ {n，1} $也是特定$ n $ n $ -ary cantor代数的一组自动形态：此$ n $ - cantor代数首先被构造为限制性semogroup-semogroup-semogroup-semogroup-la statman的总图，然后在标有标记的树木的la la la la la la la higman的范围内构造。
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 $G_{n,1}$ is the group of units of a Boolean inverse monoid $C_{n}$ called the Cuntz inverse monoid. This inverse monoid is proved to be the tight completion of the polycyclic inverse monoid $P_{n}$. The étale topological groupoid associated with $C_{n}$ under non-commutative Stone duality is the usual groupoid associated with the corresponding Cuntz $C^{\ast}$-algebra. We then show that the group $G_{n,1}$ 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 à la Statman and then in terms of labelled trees à la Higman.
