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An algebraic framework for noncommutative bundles with homogeneous fibres / Tomasz Brzezinski; Wojciech Szymański
Algebra & Number Theory, Volume: 15, Issue: 1, Pages: 217 - 240
Swansea University Author: Tomasz, Brzezinski
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DOI (Published version): 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. Th...
| Published in: | Algebra & Number Theory |
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| ISSN: | 1937-0652 1944-7833 |
| Published: |
Mathematical Sciences Publishers
2021
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| Online Access: |
Check full text
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| 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. |
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| Keywords: |
noncommutative bundle, quantum flag manifold, quantum homogeneous space, quantum twistor bundle |
| College: |
College of Science |
| Issue: |
1 |
| Start Page: |
217 |
| End Page: |
240 |