An algebraic framework for noncommutative bundles with homogeneous fibres

Abstract

An algebraic framework for noncommutative bundles with (quantum) homogeneous fibres is proposed. The framework relies on the use of principal coalgebra extensions which play the role of principal bundles in noncommutative geometry which might be additionally equipped with a Hopf algebra symmetry. The proposed framework is supported by two examples of noncommutative $\mathbb{C}{P}_q^1$-bundles: the quantum flag manifold viewed as a bundle with a generic Podleś sphere as a fibre, and the quantum twistor bundle viewed as a bundle over the quantum 4-sphere of Bonechi, Ciccoli and Tarlini.

arXiv comment21 pages

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Cited by in corpus (3)

• Gysin sequences and SU(2)-symmetries of C*-algebras
• Nichols Algebras and Quantum Principal Bundles
• Realizations of free actions via their fixed point algebras