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arXiv · 0911.0238

Fundamental group of simple $C^*$-algebras with unique trace II

Norio Nawata·Yasuo Watatani
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Abstract

We show that any countable subgroup of the multiplicative group $\mathbb{R}_+^{\times}$ of positive real numbers can be realized as the fundamental group $\mathcal{F}(A)$ of a separable simple unital $C^*$-algebra $A$ with unique trace. Furthermore for any fixed countable subgroup $G$ of $\mathbb{R}_+^{\times}$, there exist uncountably many mutually nonisomorphic such algebras $A$ with $G = \mathcal{F}(A)$.

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Norio Nawata, Yasuo Watatani. 2009-11-02. Fundamental group of simple $C^*$-algebras with unique trace II. https://arxiv.org/abs/0911.0238

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