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 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.

Keywords
noncommutative bundle, quantum homogeneous space, quantum flag manifold, quantum twistor bundle
Mathematical Subject Classification 2010
Primary: 58B32
Secondary: 16T05, 81R60
Milestones
Received: 7 December 2019
Revised: 20 June 2020
Accepted: 28 July 2020
Published: 1 March 2021
Authors
Tomasz Brzeziński
Faculty of Mathematics
University of Białystok
Białystok
Poland
Department of Mathematics
Swansea University
Swansea University Bay Campus
Swansea
United Kingdom
Wojciech Szymański
Department of Mathematics and Computer Science
University of Southern Denmark
Odense
Denmark