#### Vol. 15, No. 1, 2021

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An algebraic framework for noncommutative bundles with homogeneous fibres

### Tomasz Brzeziński and Wojciech Szymański

Vol. 15 (2021), No. 1, 217–240
##### 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 $ℂ{P}_{q}^{1}$-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.

##### Keywords
noncommutative bundle, quantum homogeneous space, quantum flag manifold, quantum twistor bundle
##### Mathematical Subject Classification 2010
Primary: 58B32
Secondary: 16T05, 81R60