Principal fibrations from noncommutative spheres

Details Principal fibrations from noncommutative spheres Principal fibrations from noncommutative spheres

2004-10-05

arxiv.org/abs/math/0410077v3

Commun.Math.Phys. 260 (2005) 203-225

Mathematics

Quantum Algebra

23 pages. Latex. v3: Additional minor corrections, version published in CMP

Scientific paper

10.1007/s00220-005-1377-7

We construct noncommutative principal fibrations S_\theta^7 \to S_\theta^4 which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated to the irreducible representations of SU(2) as modules of coequivariant maps and construct corresponding projections. The index of Dirac operators with coefficients in the associated bundles is computed with the Connes-Moscovici local index formula. The algebra inclusion $A(S_\theta^4) \into A(S_\theta^7)$ is an example of a not trivial quantum principal bundle.

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