Title | The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere |
Publication Type | Journal Article |
Year of Publication | 2008 |
Authors | D'Andrea, F, Dabrowski, L, Landi, G |
Journal | Comm. Math. Phys. 279 (2008) 77-116 |
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 quantum Euclidean 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 of the spin structure of 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. A real structure which satisfies all required properties modulo a suitable ideal of `infinitesimals\\\' is also introduced. |
URL | http://hdl.handle.net/1963/2567 |
DOI | 10.1007/s00220-008-0420-x |
Alternate Journal | The Isospectral Dirac Operator on the 4-dimensional Quantum Euclidean Sphere |
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