TY - JOUR
T1 - The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere
JF - Comm. Math. Phys. 279 (2008) 77-116
Y1 - 2008
A1 - Francesco D\'Andrea
A1 - Ludwik Dabrowski
A1 - Giovanni Landi
AB - 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.
UR - http://hdl.handle.net/1963/2567
U1 - 1553
U2 - Mathematics
U3 - Mathematical Physics
ER -