Abstract
AbstractWe 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 $.
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