Year: 2026
Type: preprint
Abstract: We show that length functions on hyperbolic groups whose induced metrics are hyperbolic and weakly geodesic naturally give rise to compact quantum metric spaces, thus generalizing the result of Ozawa and Rieffel. As a result we obtain several new examples of compact quantum metric spaces, in particular arising from Green metrics associated with random walks on hyperbolic groups, and from proper cocompact isometric actions on proper geodesic hyperbolic spaces admitting a point with trivial stabilizer.
Source: arXiv (Cornell University)
Author: Austad, Are
Institution: University of Oslo
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204778369
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