Bundles over Quantum Real Weighted Projective Spaces

Axioms

Tomasz Brzezinński¹ 

关键词: quantum real weighted projective space;    principal comodule algebra;    noncommutative line bundle;   

DOI  :  10.3390/axioms1020201

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2012 by the authors; licensee MDPI, Basel, Switzerland.