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

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

1998-12-15

arxiv.org/abs/math/9812085v1

Mathematics

Quantum Algebra

21 pages, Latex+amsmath+amssymb+amsfonts

Scientific paper

10.1016/S0393-0440(99)00014-5

Let (\Gamma,d) be the 3D-calculus or the 4D_{\pm}-calculus on the quantum group SU_q(2). We describe all pairs (\pi, F) of a *-representation \pi of 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,\pi(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.

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