01110nas a2200121   4500008004300000245008200043210006900125520069200194100002400886700002200910700002000932856003600952       2008                        en_Ud  00aThe Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere0 aIsospectral Dirac Operator on the 4dimensional Orthogonal Quantu3 aEquivariance 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.1 aD'Andrea, Francesco1 aDabrowski, Ludwik1 aLandi, Giovanni  uhttp://hdl.handle.net/1963/2567