由$β$ -展开产生的$C^*$ -代数的拓扑完全群
Topological full groups of $C^*$-algebras arising from $β$-expansions
摘要：
我们将引入一个无限非顺从离散群族$Γ_β, 1 < β\in {\mathbb{R}}$作为Higman-Thompson群$V_n, 1 < n \in {\mathbb{N}}$的一个插值，通过使用由实数的$β$ -展开定义的群胚的拓扑完全群.它们被视为某些内插Cuntz代数的完全群。如果$1$的$β$ -展开是有限的或最终周期的，则群$Γ_β, 1 < β\in {\mathbb{R}}$被实现为$[0,1]$上的分段线性函数群。利用$β$的数论性质对群$Γ_β, 1 < β\in {\mathbb{R}}$进行了分类.
英文摘要：
We will introduce a family $Γ_β, 1 < β\in {\mathbb{R}}$ of infinite non-amenable discrete groups as an interpolation of the Higman-Thompson groups $V_n, 1 < n \in {\mathbb{N}}$ by using the topological full groups of the groupoids defined by $β$-expansions of real numbers. They are regarded as full groups of certain interpolated Cuntz algebras. The groups $Γ_β, 1 < β\in {\mathbb{R}}$ are realized as groups of piecewise linear functions on $[0,1]$ if the $β$-expansion of $1$ is finite or ultimately periodic. We also classify the groups $Γ_β, 1 < β\in {\mathbb{R}}$ by the number theoretical property of $β$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
