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

Algebra & Number Theory, Volume: 15, Issue: 1, Pages: 217 - 240

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 & Number Theory
ISSN: 1937-0652 1944-7833
Published: Mathematical Sciences Publishers 2021
Online Access: Check full text

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.
Keywords: noncommutative bundle, quantum flag manifold, quantum homogeneous space, quantum twistor bundle
College: College of Science
Issue: 1
Start Page: 217
End Page: 240