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Bratteli Diagrams, Hopf–Galois Extensions and Calculi
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Edwin Beggs
Symmetry, Volume: 17, Issue: 2, Start page: 164
Swansea University Author:
Edwin Beggs
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© 2025 by the authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
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DOI (Published version): 10.3390/sym17020164
Abstract
Hopf–Galois extensions extend the idea of principal bundles to noncommutative geometry, using Hopf algebras as symmetries. We show that the matrix embeddings in Bratteli diagrams are iterated direct sums of Hopf–Galois extensions (quantum principal bundles) for certain finite abelian groups. The cor...
| Published in: | Symmetry |
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| ISSN: | 2073-8994 |
| Published: |
MDPI AG
2025
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa68985 |
| Abstract: |
Hopf–Galois extensions extend the idea of principal bundles to noncommutative geometry, using Hopf algebras as symmetries. We show that the matrix embeddings in Bratteli diagrams are iterated direct sums of Hopf–Galois extensions (quantum principal bundles) for certain finite abelian groups. The corresponding strong universal connections are computed. We show that (ℂ) is a trivial quantum principle bundle for the Hopf algebra ℂ[ℤ×ℤ]. We conclude with an application relating calculi on groups to calculi on matrices. |
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| Keywords: |
Hopf–Galois extensions; Bratteli diagrams; differential calculi |
| College: |
Faculty of Science and Engineering |
| Funders: |
The research is funded by Imam Mohammad Ibn Saud Islamic University for covering the open access fee. |
| Issue: |
2 |
| Start Page: |
164 |