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arXiv · 2310.04052

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 Dabrowski. 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 Podles spheres.

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Max Holst Mikkelsen, Jens Kaad. 2023-10-06. Spectral metrics on quantum projective spaces. https://arxiv.org/abs/2310.04052

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