We construct a quantum version of the SU(2) Hopf bundle S7→S4. The quantum sphere Sq7 arises from the symplectic group Spq(2) and a quantum 4-sphere Sq4 is obtained via a suitable self-adjoint idempotent p whose entries generate the algebra A(Sq4) 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 Sq4 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 Sq7 such that the algebra A(Sq7) is a non-trivial quantum principal bundle over A(Sq4) with structure quantum group A(SUq (2)).

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

LANDI, GIOVANNI;
2006

Abstract

We construct a quantum version of the SU(2) Hopf bundle S7→S4. The quantum sphere Sq7 arises from the symplectic group Spq(2) and a quantum 4-sphere Sq4 is obtained via a suitable self-adjoint idempotent p whose entries generate the algebra A(Sq4) 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 Sq4 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 Sq7 such that the algebra A(Sq7) is a non-trivial quantum principal bundle over A(Sq4) with structure quantum group A(SUq (2)).
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11368/1695869
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