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An algebraic framework for noncommutative bundles with homogeneous fibres / Tomasz Brzezinski; Wojciech SzymaƄski

Algebra and Number Theory

Swansea University Author: Tomasz, Brzezinski

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. Th...

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Published in: Algebra and Number Theory
URI: https://cronfa.swan.ac.uk/Record/cronfa54834
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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 Podle\'s sphere as a fibre, and the quantum twistor bundle viewed as a bundle over the quantum 4-sphere of Bonechi, Ciccoli and Tarlini.