Pythagoras Theorem in noncommutative geometry

DOI10.1090/conm/676/13611zbMath1368.58003arXiv1507.08773OpenAlexW4235691671MaRDI QIDQ2975223

Francesco D'Andrea

Publication date: 11 April 2017

Published in: Noncommutative Geometry and Optimal Transport (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.08773

zbMATH Keywords

noncommutative geometryspectral distancespectral triplesPythagoras theorem

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Noncommutative differential geometry (46L87) Noncommutative geometry (à la Connes) (58B34)

Related Items (4)

Revisiting Connes’ finite spectral distance on noncommutative spaces: Moyal plane and fuzzy sphere ⋮ A dual formula for the spectral distance in noncommutative geometry ⋮ Reconstructing manifolds from truncations of spectral triples ⋮ Non-associative geometry of quantum tori

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Pythagoras theorem for products of spectral triples
• Noncommutative geometry of the Moyal plane: translation isometries, Connes' distance on coherent states, Pythagoras equality
• Leibniz seminorms and best approximation from \(C^*\)-subalgebras
• A view on optimal transport from noncommutative geometry
• The spectral distance in the Moyal plane
• Noncommutative geometry, quantum fields and motives
• Mass transportation problems. Vol. 1: Theory. Vol. 2: Applications
• Optimal transportation and applications. Lectures given at the C. I. M. E. summer school, Martina Franca, Italy, September 2--8, 2001
• Metrics on state spaces
• Metric properties of the fuzzy sphere
• Noncommutative geometry and particle physics
• Spectral geometry with a cut-off: topological and metric aspects
• The Monge metric on the sphere and geometry of quantum states
• Introduction to Smooth Manifolds
• Matrix geometries emergent from a point
• Gromov-Hausdorff distance for quantum metric spaces
• Discrete Kaluza–Klein from scalar fluctuations in noncommutative geometry
• Spectral triplets, statistical mechanics and emergent geometry in non-commutative quantum mechanics
• Geometry of Quantum States
• Quantum Information Processing with Finite Resources
• Optimal Transport
• Encyclopedia of Distances
• Disctances in finite spaces from noncommutative geometry

This page was built for publication: Pythagoras Theorem in noncommutative geometry