2002/11/29 by F. Bonechi, Francesco Bonechi, Nicola Ciccoli +2 · 7 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Canonical quantization #Cohomology #Degenerate energy levels #Equivariant cohomology #Geometric quantization #Homology (biology) #Homotopy #Homotopy and Cohomology in Algebraic Topology #Iterated function #Mathematical analysis #Mathematics #Physics #Poisson manifold #Pure mathematics #Quantization (signal processing) #Quantum #Quantum cohomology #Quantum mechanics #SPHERES #Suspension (topology) #Symplectic geometry #hep-th #math.KT #math.OA #math.QA #msc:14D21 #msc:19D55 #msc:58B32 #msc:58B34 #msc:81R50
paper · pdf · doi:10.1007/s00220-003-0971-9
published in Communications in Mathematical Physics 243(3), 449-459 (Springer Science+Business Media) · 13 pages; LaTeX 2e
arxiv created 2002/11/29 · openalex publication_date 2003/12/01 · arxiv updated 2010/04/23 · openalex created_date 2016/07/22 · openalex updated_date 2026/08/05
We define even dimensional quantum spheres Sigmaq2n that generalize to higher dimension the standard quantum two-sphere of Podle's and the four-sphere Sigmaq4 obtained in the quantization of the Hopf bundle. The construction relies on an iterated Poisson double suspension of the standard Podle's two-sphere. The Poisson spheres that we get have the same symplectic foliation consisting of a degenerate point and a symplectic plane and, after quantization, have the same C^*-algebraic completion. We investigate their K-homology and K-theory by introducing Fredholm modules and projectors.