Characterization of SU q (ℓ + 1)-equivariant spectral triples for the odd dimensional quantum spheres

DOI10.1515/CRELLE.2008.071zbMath1158.58003arXivmath/0701694OpenAlexW2155562080MaRDI QIDQ3542071

Partha Sarathi Chakraborty, Arup Kumar Pal

Publication date: 27 November 2008

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701694

zbMATH Keywords

quantum spherespectral triplecombinatorial methodClebsh-Gordan coefficientsGelfand-Tsetlin tableauxoptimum family

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) Geometry of quantum groups (58B32) Noncommutative geometry (à la Connes) (58B34)

Related Items (15)

Quantum quaternion spheres ⋮ An invariant for homogeneous spaces of compact quantum groups ⋮ Unnamed Item ⋮ Topological invariance of quantum quaternion spheres ⋮ Equivariant spectral triples for homogeneous spaces of the compact quantum group \(U_q(2)\) ⋮ Smooth dense subalgebras and Fourier multipliers on compact quantum groups ⋮ Torus equivariant spectral triples for odd-dimensional quantum spheres coming from \(C^{*}\)-extensions ⋮ Equivariant spectral triple for the quantum group \(U_q(2)\) for complex deformation parameters ⋮ Noncommutative complex geometry of the quantum projective space ⋮ Spectral metric spaces on extensions of \(C^*\)-algebras ⋮ Quantum double suspension and spectral triples ⋮ Equivariant spectral triples and Poincaré duality for 𝑆𝑈_{𝑞}(2) ⋮ Regularity and dimension spectrum of the equivariant spectral triple for the odd-dimensional quantum spheres ⋮ Operator algebras in India in the past decade ⋮ Hopf coactions on odd spheres

Cites Work

• Fredholm modules for quantum Euclidean spheres
• Gravity coupled with matter and the foundation of non-commutative geometry
• The Dirac operator on \(\text{SU}_{q}(2)\)
• Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups
• Equivariant spectral triples on the quantum SU(2) group
• Construction of dynamical quadratic algebras
• Quantum spheres and projective spaces as graph algebras
• Symmetries of quantum spaces. Subgroups and quotient spaces of quantum \(SU(2)\) and \(SO(3)\) groups
• The local index formula in noncommutative geometry
• The local index formula for \(\text{SU}_{q}(2)\)
• Algèbres enveloppantes quantifiées, groupes quantiques compacts de matrices et calcul différentiel non commutatif. (Quantized enveloping algebras, compact quantum matrix groups and noncommutative differential calculus)
• CYCLIC COHOMOLOGY, QUANTUM GROUP SYMMETRIES AND THE LOCAL INDEX FORMULA FOR SU q (2)

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