Spectral metrics on quantum projective spaces

Max Holst Mikkelsen, Jens Kaad*

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Abstract

We show that the noncommutative differential geometry of quantum projective spaces is compatible with Rieffel's theory of compact quantum metric spaces. This amounts to a detailed investigation of the Connes metric coming from the unital spectral triple introduced by D'Andrea and Dąbrowski. In particular, we establish that the Connes metric metrizes the weak-⁎ topology on the state space of quantum projective space. This generalizes previous work by the second author and Aguilar regarding spectral metrics on the standard Podleś spheres.
OriginalsprogEngelsk
Artikelnummer110466
TidsskriftJournal of Functional Analysis
Vol/bind287
Udgave nummer2
Antal sider38
ISSN0022-1236
DOI
StatusUdgivet - 15. jul. 2024

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