An algebraic framework for noncommutative bundles with homogeneous fibres

Tomasz Brzeziński, Wojciech Szymanski

Research output: Contribution to journalJournal articleResearchpeer-review

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 Pq 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.

Original languageEnglish
JournalAlgebra & Number Theory
Volume15
Issue number1
Pages (from-to)217-240
ISSN1937-0652
DOIs
Publication statusPublished - 2021

Keywords

  • noncommutative fibre bundle
  • coalgebra
  • Hopf-Galois extension
  • Quantum homogeneous space
  • Quantum flag manifold
  • Quantum twistor bundle
  • Noncommutative bundle

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