Abstract:We consider a natural CQMS structure on a twisted transformation groupoid $C^{\ast}$-algebra coming from stratified $_{\text {c}}$Lip-norm introduced by Austad. We obtain upper bounds of metric dimension of reduced $C^{\ast}$-algebra of a transformation groupoid $\Gamma\rtimes X$ and its cocycle twist for a suitably chosen CQMS structure, provided $(X,d)$ is a compact metric space of finite Kolmogorov dimension and $\Gamma$ is a discrete group of polynomial growth. When $\Gamma$ has exponential growth, we prove that the dimension is generically $+\infty$ proving that the dichotomy between polynomial growth and exponential growth of groups survive even after considering cocycle twists of transformation groupoids.
From: Arnab Chattopadhyay [view email]
[v1]
Tue, 23 Jun 2026 15:52:35 UTC (41 KB)
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