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Dirac operators on the quantum group SU(2) and the quantum sphere. (English. Russian original) Zbl 0954.58004
J. Math. Sci., New York 100, No. 2, 2039-2050 (2000); translation from Zap. Nauchn. Semin. POMI 245, 49-65 (1997).
Summary: The problem of constructing the Dirac operators on the quantum group SU(2) and the quantum sphere \(S^2_{q\mu}\) are discussed. In both cases, the constructions presented have the same \(SU_q(2)\)-invariant form and are directly connected with the corresponding Laplace operators.

MSC:
58B32 Geometry of quantum groups
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
17B37 Quantum groups (quantized enveloping algebras) and related deformations
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
46L87 Noncommutative differential geometry
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