2006/11/30 by Francesco D’Andrea, Francesco D'Andrea, Ludwik Dabrowski +2 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #hep-th #math.QA #msc:58B32 #msc:58B34
paper · pdf · doi:10.1007/s00220-008-0420-x
published as Commun. Math. Phys. 279 (2008) 77--116 · 40 pages, no figures, Latex. v2: Title changed. Sect. 9 on real structure completely rewritten and results strengthened. Additional minor changes throughout the paper
openalex publication_date 2008/02/07 · arxiv created 2008/02/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
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 S4q. 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.