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Bundles over Quantum RealWeighted Projective Spaces
Department of Mathematics, Swansea University, Singleton Park, Swansea SA2 8PP, UK
* Author to whom correspondence should be addressed.
Received: 10 July 2012; in revised form: 21 August 2012 / Accepted: 23 August 2012 / Published: 17 September 2012
Abstract: The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1)-bundles over quantum real weighted projective spaces are constructed. As the spaces in question fall into two separate classes, the negative or odd class that generalises quantum real projective planes and the positive or even class that generalises the quantum disc, so do the constructed principal bundles. In the negative case the principal bundle is proven to be non-trivial and associated projective modules are described. In the positive case the principal bundles turn out to be trivial, and so all the associated modules are free. It is also shown that the circle (co)actions on the quantum Seifert manifold that define quantum real weighted projective spaces are almost free.
Keywords: quantum real weighted projective space; principal comodule algebra; noncommutative line bundle
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Cite This Article
MDPI and ACS Style
Brzeziński, T.; Fairfax, S.A. Bundles over Quantum RealWeighted Projective Spaces. Axioms 2012, 1, 201-225.
Brzeziński T, Fairfax SA. Bundles over Quantum RealWeighted Projective Spaces. Axioms. 2012; 1(2):201-225.
Brzeziński, Tomasz; Fairfax, Simon A. 2012. "Bundles over Quantum RealWeighted Projective Spaces." Axioms 1, no. 2: 201-225.