2012
DOI: 10.1016/j.geomphys.2011.12.008
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Quantum principal bundles over quantum real projective spaces

Abstract: Abstract. Two hierarchies of quantum principal bundles over quantum real projective spaces are constructed. One hierarchy contains bundles with U (1) as a structure group, the other has the quantum group SU q (2) as a fibre. Both hierarchies are obtained by the process of prolongation from bundles with the cyclic group of order 2 as a fibre. The triviality or otherwise of these bundles is determined by using a general criterion for a prolongation of a comodule algebra to be a cleft Hopf-Galois extension.

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Cited by 18 publications
(33 citation statements)
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References 26 publications
(53 reference statements)
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“…Proof. As explained in [2] O(Σ 3 q (1, 1)) is a prolongation of the CZ 2 -comodule algebra O(S 2 q ). The latter is a principal comodule algebra (over the quantum real projective plane O(RP 2 q ) [14]) and since a prolongation of a principal comodule algebra is a principal comodule algebra [8, Remark 3.11], the coaction 1,1 is principal as stated.…”
Section: Quantum Real Weighted Projective Spaces and Quantum Principamentioning
confidence: 95%
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“…Proof. As explained in [2] O(Σ 3 q (1, 1)) is a prolongation of the CZ 2 -comodule algebra O(S 2 q ). The latter is a principal comodule algebra (over the quantum real projective plane O(RP 2 q ) [14]) and since a prolongation of a principal comodule algebra is a principal comodule algebra [8, Remark 3.11], the coaction 1,1 is principal as stated.…”
Section: Quantum Real Weighted Projective Spaces and Quantum Principamentioning
confidence: 95%
“…is surjective, and write [2] for the C-linear map such that can( (h)) = 1 ⊗ h, for all h ∈ H. Then, by the Schneider theorem [8], A is a principal H-comodule algebra. Explicitly, a strong connection form is…”
Section: Example 218mentioning
confidence: 99%
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“…Then A is called principal H-comodule algebra (c.f. [6]) whenever there exists a C-linear unital map By quantum principal bundle we shall understand the structure defined as above, and we shall often denote it simply by the inclusion map B ֒→ A. Moreover, we shall call the map ℓ strong connection lift.…”
Section: Quantum Principal U (1)-bundlesmentioning
confidence: 99%