*-compatible connections in noncommutative Riemannian geometry

DOI10.1016/j.geomphys.2010.09.002zbMath1211.53092arXiv0904.0539OpenAlexW2964241782WikidataQ115353313 ScholiaQ115353313MaRDI QIDQ617941

Edwin J. Beggs, Shahn Majid

Publication date: 14 January 2011

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

Full work available at URL: https://arxiv.org/abs/0904.0539

zbMATH Keywords

Riemannian geometryquantum groupnoncommutative geometrydifferential graded algebraLevi-Civita connection\(^*\)-algebra

Mathematics Subject Classification ID

Applications of global differential geometry to the sciences (53C80) Global Riemannian geometry, including pinching (53C20) Noncommutative global analysis, noncommutative residues (58J42)

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Cites Work

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• Bar categories and star operations
• The Serre spectral sequence of a noncommutative fibration for de Rham cohomology
• Quantum and braided group Riemannian geometry
• Quantum group gauge theory on quantum spaces
• Leibniz rules and reality conditions
• Noncommutative Riemannian and spin geometry of the standard \(q\)-sphere
• Differential calculus on compact matrix pseudogroups (quantum groups)
• Connections on central bimodules in noncommutative differential geometry
• Linear connections on the quantum plane
• On the first-order operators in bimodules
• Non-commutative geometry of finite groups
• Linear connections in non-commutative geometry
• Linear connections on matrix geometries
• Linear connections on extended space-time
• Linear connections on fuzzy manifolds
• Riemannian geometry of quantum groups and finite groups with nonuniversal differentials

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