Communications in Mathematical Physics

, Volume 263, Issue 1, pp 65–88 | Cite as

A Hopf Bundle Over a Quantum Four-Sphere from the Symplectic Group

  • Giovanni LandiEmail author
  • Chiara Pagani
  • Cesare Reina


We construct a quantum version of the SU(2) Hopf bundle S 7S 4. The quantum sphere S 7 q arises from the symplectic group Sp q (2) and a quantum 4-sphere S 4 q is obtained via a suitable self-adjoint idempotent p whose entries generate the algebra A(S 4 q ) of polynomial functions over it. This projection determines a deformation of an (anti-)instanton bundle over the classical sphere S 4. We compute the fundamental K-homology class of S 4 q and pair it with the class of p in the K-theory getting the value −1 for the topological charge. There is a right coaction of SU q (2) on S 7 q such that the algebra A(S 7 q ) is a non-trivial quantum principal bundle over A(S 4 q ) with structure quantum group A(SU q (2)).


Neural Network Statistical Physic Complex System Nonlinear Dynamics Polynomial Function 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità di TriesteTriesteItaly
  2. 2.S.I.S.S.A. International School for Advanced StudiesTriesteItaly
  3. 3.I.N.F.NNapoliItaly

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