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arXiv · 2003.04765

A torsion-free algebraically C*-unique group

Eduardo Scarparo
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Abstract

Let $p$ and $q$ be multiplicatively independent integers. We show that the complex group ring of $\mathbb{Z}[\frac{1}{pq}]\rtimes\mathbb{Z}^2$ admits a unique $\mathrm{C}^*$-norm. The proof uses a characterization, due to Furstenberg, of closed $\times p-$ and $\times q-$invariant subsets of $\mathbb{T}$.

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Eduardo Scarparo. 2020-03-10. A torsion-free algebraically C*-unique group. https://doi.org/10.1216/rmj.2020.50.1813

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