Commutator representations of differential calculi on the quantum group \(SU_q(2)\)

DOI10.1016/S0393-0440(99)00014-5zbMath1016.17014arXivmath/9812085OpenAlexW3099431673WikidataQ115338763 ScholiaQ115338763MaRDI QIDQ1125218

Konrad Schmüdgen

Publication date: 15 February 2000

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

Full work available at URL: https://arxiv.org/abs/math/9812085

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)

Related Items (11)

The Dirac operator on \(\text{SU}_{q}(2)\) ⋮ Quantum groups, differential calculi and the eigenvalues of the Laplacian ⋮ Twisted cyclic homology of all Podleś quantum spheres ⋮ Twisted Dirac Operator on Quantum SU(2) in Disc Coordinates ⋮ An operator-theoretic approach to invariant integrals on quantum homogeneous \(\text{SU}_{n,1}\)-spaces ⋮ THE 3D SPIN GEOMETRY OF THE QUANTUM TWO-SPHERE ⋮ Spectral action on \(\mathrm{SU}_q(2)\) ⋮ On the noncommutative spin geometry of the standard Podleś sphere and index computations ⋮ HODGE DUALITY OPERATORS ON LEFT-COVARIANT EXTERIOR ALGEBRAS OVER TWO- AND THREE-DIMENSIONAL QUANTUM SPHERES ⋮ A local index formula for the quantum sphere ⋮ Spectral triples and differential calculi related to the Kronecker foliation

Cites Work

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• Quantum spheres
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Representations of the quantum group \(SU_ q(2)\) and the little q-Jacobi polynomials
• Classification of three-dimensional covariant differential calculi on Podles' quantum spheres and on related spaces
• Differential calculus on compact matrix pseudogroups (quantum groups)
• Algebra of functions on the quantum group SU(2)
• Left-covariant differential calculi on \(\mathrm{SL}_q(2)\) and \(\mathrm{SL}_q(3)\)
• Classification of bicovariant differential calculi on the quantum groups SLq(n+1) and Spq(2n)

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