An algebraic framework for noncommutative bundles with homogeneous fibres

Brzeziński, Tomasz; Szymański, Wojciech

doi:10.2140/ant.2021.15.217

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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

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 $ℂ P_{q}^{1}$ -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

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

Vol. 15, No. 1, 2021