The Podleś sphere as a spectral metric space

DOI10.1016/j.geomphys.2018.07.015zbMath1403.58004arXiv1803.03027OpenAlexW2792584376MaRDI QIDQ1788815

Konrad Aguilar, Jens Kaad

Publication date: 8 October 2018

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.03027

zbMATH Keywords

Podleś spherespectral tripleslip-normsquantum metric spaces

Mathematics Subject Classification ID

Geometry of quantum groups (58B32) Isospectrality (58J53)

Related Items (11)

Polynomial approximation of quantum Lipschitz functions ⋮ The Podleś spheres converge to the sphere ⋮ The Gromov-Hausdorff propinquity for metric spectral triples ⋮ Convergence of Fourier truncations for compact quantum groups and finitely generated groups ⋮ Convergence of inductive sequences of spectral triples for the spectral propinquity ⋮ Heisenberg Modules over Quantum 2-tori are Metrized Quantum Vector Bundles ⋮ Convergence of spectral triples on fuzzy tori to spectral triples on quantum tori ⋮ INDUCTIVE LIMITS OF C*-ALGEBRAS AND COMPACT QUANTUM METRIC SPACES ⋮ Gromov-Hausdorff convergence of quantised intervals ⋮ The dual modular Gromov-Hausdorff propinquity and completeness ⋮ Actions of categories by Lipschitz morphisms on limits for the Gromov-Hausdorff propinquity

Cites Work

• Gravity coupled with matter and the foundation of non-commutative geometry
• Dirac operators on all Podleś quantum spheres
• Quantum spheres
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Metrics on states from actions of compact groups
• Metrics on state spaces
• The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podleś sphere
• A local index formula for the quantum sphere
• A residue formula for the fundamental Hochschild class on the Podleś sphere
• Hyperbolic Group C^*-Algebras and Free-Product C^*-Algebras as Compact Quantum Metric Spaces
• The quantum Gromov-Hausdorff propinquity
• Gromov-Hausdorff distance for quantum metric spaces
• Dirac operator and a twisted cyclic cocycle on the standard Podles quantum sphere
• Matricial bridges for “Matrix algebras converge to the sphere”
• Compact metric spaces, Fredholm modules, and hyperfiniteness
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