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The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere

Francesco D'Andrea·Ludwik Dabrowski·Giovanni Landi
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Abstract

Equivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the orthogonal quantum 4-sphere S^4_q. These representations are the constituents of a spectral triple on this sphere with a Dirac operator which is isospectral to the canonical one on the round undeformed four-sphere and which gives metric dimension four for the noncommutative geometry. Non-triviality of the geometry is proved by pairing the associated Fredholm module with an `instanton' projection. We also introduce a real structure which satisfies all required properties modulo smoothing operators.

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Francesco D'Andrea, Ludwik Dabrowski, Giovanni Landi. 2008-02-13. The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere. https://doi.org/10.1007/s00220-008-0420-x

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