Curved Noncommutative Tori as Leibniz Quantum Compact Metric Spaces

Abstract

We prove that curved noncommutative tori, introduced by Dabrowski and Sitarz, are Leibniz quantum compact metric spaces and that they form a continuous family over the group of invertible matrices with entries in the commutant of the quantum tori in the regular representation, when this group is endowed with a natural length function.

16 Pages, v3: accepted in Journal of Math. Physics

References in corpus (3)

• Type III and spectral triples
• Matricial bridges for "Matrix algebras converge to the sphere"
• C*-algebraic quantum Gromov-Hausdorff distance

Cited by in corpus (5)

• Twisted reality condition for Dirac operators
• Continuity of the Spectrum of Dirac Operators of Spectral Triples for the Spectral Propinquity
• Vietoris topology on hyperspaces associated to a noncommutative compact space
• Convergence of Spectral Triples on Fuzzy Tori to Spectral Triples on Quantum Tori
• Metrized Quantum Vector Bundles over Quantum Tori Built from Riemannian Metrics and Rosenberg's Levi-Civita Connections