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2021 An algebraic framework for noncommutative bundles with homogeneous fibres
Tomasz Brzeziński, Wojciech Szymański
Algebra Number Theory 15(1): 217-240 (2021). DOI: 10.2140/ant.2021.15.217

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 Pq1-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.

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Tomasz Brzeziński. Wojciech Szymański. "An algebraic framework for noncommutative bundles with homogeneous fibres." Algebra Number Theory 15 (1) 217 - 240, 2021. https://doi.org/10.2140/ant.2021.15.217

Information

Received: 7 December 2019; Revised: 20 June 2020; Accepted: 28 July 2020; Published: 2021
First available in Project Euclid: 17 March 2021

Digital Object Identifier: 10.2140/ant.2021.15.217

Subjects:
Primary: 58B32
Secondary: 16T05 , 81R60

Keywords: noncommutative bundle , quantum flag manifold , quantum homogeneous space , quantum twistor bundle

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.15 • No. 1 • 2021
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