Connections on Lie algebroids and on derivation-based noncommutative geometry

DOI10.1016/j.geomphys.2011.11.002zbMath1260.58002arXiv1003.6106OpenAlexW1918536288WikidataQ71433651 ScholiaQ71433651MaRDI QIDQ2428161

Serge Lazzarini, Thierry Masson

Publication date: 24 April 2012

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

Full work available at URL: https://arxiv.org/abs/1003.6106

zbMATH Keywords

noncommutative geometrydifferential geometryconnectiondifferential algebraLie algebroid

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) Yang-Mills and other gauge theories in quantum field theory (81T13) Pseudogroups and differentiable groupoids (58H05) Noncommutative geometry (à la Connes) (58B34) Connections (general theory) (53C05)

Related Items (10)

Braided Cartan calculi and submanifold algebras ⋮ Universal corner symmetry and the orbit method for gravity ⋮ BRST cohomology is Lie algebroid cohomology ⋮ Crossed products, extended phase spaces and the resolution of entanglement singularities ⋮ Extended phase space in general gauge theories ⋮ Derivation-based noncommutative field theories on AF algebras ⋮ Lie algebroids and the geometry of off-shell BRST ⋮ Gauge invariant composite fields out of connections, with examples ⋮ Extending tangent bundles by an algebra bundle ⋮ Cartan connections and Atiyah Lie algebroids

Cites Work

• Noncommutative Yang-Mills-Higgs actions from derivation-based differential calculus
• \(SU(n)\)-connections and noncommutative differential geometry
• Invariants of Lie algebroids
• Differentiable and algebroid cohomology, Van Est isomorphisms, and characteristic classes
• On the noncommutative geometry of the endomorphism algebra of a vector bundle
• Lie algebroids, holonomy and characteristic classes
• Gravity and the standard model with neutrino mixing
• EQUIVARIANT POISSON COHOMOLOGY AND A SPECTRAL SEQUENCE ASSOCIATED WITH A MOMENT MAP
• Representations up to homotopy of Lie algebroids
• Complex Analytic Connections in Fibre Bundles
• Noncommutative differential geometry of matrix algebras
• Symplectic groupoids and Poisson manifolds
• Particle models and noncommutative geometry
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