Let $G$ be an acylindrically hyperbolic group. We prove that if $G$ has no non-trivial finite normal subgroups, then the set of invertible elements is dense in the reduced $C^\ast$-algebra of $G$. The same result is obtained for finite direct products of acylindrically hyperbolic groups.

中文翻译：

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关于圆柱双曲群的约化 C⁎-代数中的可逆元

令 $G$ 是一个圆柱双曲群。我们证明，如果$G$没有非平凡有限正规子群，那么可逆元素集在$G$的约简$C^\ast$-代数中是稠密的。对于圆柱双曲群的有限直积，也获得了相同的结果。