HODGE DUALITY OPERATORS ON LEFT-COVARIANT EXTERIOR ALGEBRAS OVER TWO- AND THREE-DIMENSIONAL QUANTUM SPHERES

DOI10.1142/S0129055X13500098zbMath1301.58003arXiv1112.6383MaRDI QIDQ2846895

Alessandro Zampini

Publication date: 3 September 2013

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

Full work available at URL: https://arxiv.org/abs/1112.6383

zbMATH Keywords

Laplaciansdifferential calculi on quantum groupsquantum 2-spherequantum Hopf fibrationHodge operators

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 differential geometry (46L87) Geometry of quantum groups (58B32) Noncommutative global analysis, noncommutative residues (58J42) Ring-theoretic aspects of quantum groups (16T20)

Related Items

A Hodge–de Rham Dirac operator on the quantum SU(2) ⋮ Dirac operators on the S3 and S2 spheres ⋮ Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces ⋮ Warped products and Yang-Mills equations on noncommutative spaces

Cites Work

• Unnamed Item
• Unnamed Item
• (A class of) Hodge duality operators over the quantum \(\mathrm{SU}(2)\)
• *-compatible connections in noncommutative Riemannian geometry
• Gauged Laplacians on quantum Hopf bundles
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Commutator representations of differential calculi on the quantum group \(SU_q(2)\)
• The classification of differential structures on quantum 2-spheres
• Quantum and braided group Riemannian geometry
• Classification of three-dimensional covariant differential calculi on Podles' quantum spheres and on related spaces
• Noncommutative Riemannian and spin geometry of the standard \(q\)-sphere
• Differential calculus on compact matrix pseudogroups (quantum groups)
• Spin geometry on quantum groups via covariant differential calculi
• De Rham Cohomology and Hodge Decomposition For Quantum Groups
• Laplacians and gauged Laplacians on a quantum Hopf bundle
• EXAMPLES OF HODGE LAPLACIANS ON QUANTUM SPHERES
• CALCULI, HODGE OPERATORS AND LAPLACIANS ON A QUANTUM HOPF FIBRATION
• Quantum groups, differential calculi and the eigenvalues of the Laplacian
• Classification of left-covariant differential calculi on the quantum group SL\(_q(2)\)
• Riemannian geometry of quantum groups and finite groups with nonuniversal differentials