Quantum groups, differential calculi and the eigenvalues of the Laplacian

DOI10.1090/S0002-9947-05-03971-1zbMath1082.58005arXivmath/0111042OpenAlexW1992494805MaRDI QIDQ5313304

Lars Tuset, J. Kustermans, Gerard J. Murphy

Publication date: 29 August 2005

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0111042

zbMATH Keywords

noncommutative geometryHodge decompositionLaplaciandifferential calculuscompact quantum groupHodge operator

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Geometry of quantum groups (58B32) Noncommutative geometry (à la Connes) (58B34)

Related Items (8)

Hodge star as braided Fourier transform ⋮ EXAMPLES OF HODGE LAPLACIANS ON QUANTUM SPHERES ⋮ Noncommutative Kähler structures on quantum homogeneous spaces ⋮ (A class of) Hodge duality operators over the quantum \(\mathrm{SU}(2)\) ⋮ A Hodge–de Rham Dirac operator on the quantum SU(2) ⋮ A Dolbeault-Dirac spectral triple for quantum projective space ⋮ CALCULI, HODGE OPERATORS AND LAPLACIANS ON A QUANTUM HOPF FIBRATION ⋮ HODGE DUALITY OPERATORS ON LEFT-COVARIANT EXTERIOR ALGEBRAS OVER TWO- AND THREE-DIMENSIONAL QUANTUM SPHERES

Cites Work

• Compact matrix pseudogroups
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Commutator representations of differential calculi on the quantum group \(SU_q(2)\)
• An algebraic framework for group duality
• Quantum harmonic analysis and geometric invariants
• Commutator representations of covariant differential calculi on quantum groups
• Differential calculus on compact matrix pseudogroups (quantum groups)
• Differential calculi over quantum groups and twisted cyclic cocycles
• De Rham Cohomology and Hodge Decomposition For Quantum Groups
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