A Hopf Bundle Over a Quantum Four-Sphere from the Symplectic Group
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- Landi, G., Pagani, C. & Reina, C. Commun. Math. Phys. (2006) 263: 65. doi:10.1007/s00220-005-1494-3
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We construct a quantum version of the SU(2) Hopf bundle S7→S4. The quantum sphere S7q arises from the symplectic group Spq(2) and a quantum 4-sphere S4q is obtained via a suitable self-adjoint idempotent p whose entries generate the algebra A(S4q) of polynomial functions over it. This projection determines a deformation of an (anti-)instanton bundle over the classical sphere S4. We compute the fundamental K-homology class of S4q 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 SUq(2) on S7q such that the algebra A(S7q) is a non-trivial quantum principal bundle over A(S4q) with structure quantum group A(SUq(2)).