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TOPOLOGICAL FULL GROUPS OF
$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}C^*$-ALGEBRAS ARISING FROM 
$\beta $-EXPANSIONS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 97 / Issue 2 / October 2014
- Published online by Cambridge University Press:
- 17 July 2014, pp. 257-287
- Print publication:
- October 2014
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- Article
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- You have access
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We introduce a family of infinite nonamenable discrete groups as an interpolation of the Higman–Thompson groups by using the topological full groups of the groupoids defined by
$\beta $-expansions of real numbers. They are regarded as full groups of certain interpolated Cuntz algebras, and realized as groups of piecewise-linear functions on the unit interval in the real line if the 
$\beta $-expansion of 
$1$ is finite or ultimately periodic. We also classify them by a number-theoretical property of 
$\beta $.
