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

TitleThe Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere
Publication TypeJournal Article
Year of Publication2008
AuthorsD\'Andrea, F, Dabrowski, L, Landi, G
JournalComm. 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.

URLhttp://hdl.handle.net/1963/2567
DOI10.1007/s00220-008-0420-x
Alternate JournalThe Isospectral Dirac Operator on the 4-dimensional Quantum Euclidean Sphere

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