Quandles from gauge transformations
Group Theory
2026-04-21 v1 Quantum Algebra
Abstract
In this paper, we investigate a quandle structure induced by an augmented rack arising from a gauge transformation group. We construct a quandle from a principal bundle and its discrete generalization. When we see a group as a (discrete) principal bundle over a point, this quandle becomes equivalent to the generalized Alexander quandle for its inner automorphism. Moreover, we construct a Lie and Noether quandle structure from a smooth gauge transformation.
Keywords
Cite
@article{arxiv.2604.17447,
title = {Quandles from gauge transformations},
author = {Ryo Hayami},
journal= {arXiv preprint arXiv:2604.17447},
year = {2026}
}
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9 pages