THE NONCOMMUTATIVE GEOMETRY OF THE QUANTUM PROJECTIVE PLANE

DOI10.1142/S0129055X08003493zbMath1155.81024arXiv0712.3401OpenAlexW3098885393MaRDI QIDQ3602246

Francesco D'Andrea, Ludwik Dąbrowski, Giovanni Landi

Publication date: 12 February 2009

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.3401

zbMATH Keywords

noncommutative geometryquantum groupsquantum homogeneous spacesspectral triples

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Noncommutative geometry in quantum theory (81R60) Noncommutative geometry (à la Connes) (58B34)

Related Items (17)

Dolbeault-Dirac operators, quantum Clifford algebras and the Parthasarathy formula ⋮ Quantum Riemannian geometry of quantum projective spaces ⋮ A Dolbeault-Dirac spectral triple for the \(B_2\)-irreducible quantum flag manifold ⋮ Noncommutative Kähler structures on quantum homogeneous spaces ⋮ Non-commutative complex differential geometry ⋮ The homogeneous coordinate ring of the quantum projective plane ⋮ Differential and holomorphic differential operators on noncommutative algebras ⋮ A Dolbeault-Dirac spectral triple for quantum projective space ⋮ Noncommutative complex geometry of the quantum projective space ⋮ Liberations and twists of real and complex spheres ⋮ Quantum weighted projective and Lens spaces ⋮ Dirac operators on quantum projective spaces ⋮ Quantum bundle description of quantum projective spaces ⋮ Anti-selfdual connections on the quantum projective plane: monopoles ⋮ Anti-selfdual connections on the quantum projective plane: instantons ⋮ On the Dolbeault-Dirac operators on quantum projective spaces ⋮ A residue formula for the fundamental Hochschild class on the Podleś sphere

Cites Work

• The spectral geometry of the equatorial Podleś sphere
• The Dirac operator on \(\text{SU}_{q}(2)\)
• The isospectral Dirac operator on the 4-dimensional orthogonal quantum sphere
• Noncommutative geometry and the regularization problem of 4D quantum field theory
• Equivariant spectral triples on the quantum SU(2) group
• Dirac operators on quantum flag manifolds
• Projective quantum spaces
• A local index formula for the quantum sphere
• Casimir operators of U q sl(3)
• Non-integrable representations of the restricted quantum analogue ofsl(3)
• The locally finite part of the dual coalgebra of quantized irreducible flag manifolds
• Differential calculus on quantum projective spaces

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