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 $ℂP_q^1$-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.

中文翻译：

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具有均质纤维的非交换束的代数框架

提出了具有（量子）均质纤维的非交换束的代数框架。该框架依赖于使用主等分代数扩展，这些扩展在非交换几何中起主要束的作用，可交换性还可以配备霍普夫代数对称性。提议的框架由两个非交换的示例支持$ℂP_q^{\mathrm{1个}}$-束：量子标记流形被视为束，而普通的Podleś球为纤维，而量子扭转束被视为在Bonechi，Ciccoli和Tarlini的量子4球上的束。