Commutator Representations of Differential Calculi on the Quantum Group SU_q(2)

Abstract

Let (Γ,d) be the 3D-calculus or the 4D_{\pm}-calculus on the quantum group SU_q(2). We describe all pairs (π, F) of a *-representation πof O(SU_q(2)) and of a symmetric operator F on the representation space satisfying a technical condition concerning its domain such that there exist a homomorphism of first order differential calculi which maps dx into the commutator [iF,π(x)] for x\in O(SU_q(2)). As an application commutator representations of the 2-dimensional left-covariant calculus on Podles' quantum 2-sphere S^2_{qc} with c=0 are given.

21 pages, Latex+amsmath+amssymb+amsfonts

Cited by in corpus (8)

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• A Local Index Formula for the Quantum Sphere
• Twisted cyclic homology of all Podles quantum spheres
• The 3D Spin Geometry of the Quantum Two-Sphere
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• More noncommutative 4-spheres
• Geometric foundations for classical $\mathrm{U}(1)$-gauge theory on noncommutative manifolds
• Spectral triples and differential calculi related to the Kronecker foliation