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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
On the Relationship between Classical and Deformed Hopf Fibrations
Tomasz Brzezińskiab, James Gauntc, Alexander Schenkelc a Faculty of Mathematics, University of Białystok,
K. Ciołkowskiego 1M, 15-245 Białystok, Poland
b Department of Mathematics, Swansea University, Swansea University Bay Campus, Fabian Way, Swansea SA1 8EN, UK
c School of Mathematical Sciences, University of Nottingham,
University Park, Nottingham NG7 2RD, UK
Аннотация:
The $\theta$-deformed Hopf fibration $\mathbb{S}^3_\theta\to \mathbb{S}^2$ over the commutative $2$-sphere is compared with its classical counterpart. It is shown that there exists a natural isomorphism between the corresponding associated module functors and that the affine spaces of classical and deformed connections are isomorphic. The latter isomorphism is equivariant under an appropriate notion of infinitesimal gauge transformations in these contexts. Gauge transformations and connections on associated modules are studied and are shown to be sensitive to the deformation parameter. A homotopy theoretic explanation for the existence of a close relationship between the classical and deformed Hopf fibrations is proposed.
Ключевые слова:
noncommutative geometry, principal comodule algebras, noncommutative principal bundles, Hopf fibrations, homotopy equivalence.
Поступила: 17 сентября 2019 г.; в окончательном варианте 17 февраля 2020 г.; опубликована 23 февраля 2020 г.
Образец цитирования:
Tomasz Brzeziński, James Gaunt, Alexander Schenkel, “On the Relationship between Classical and Deformed Hopf Fibrations”, SIGMA, 16 (2020), 008, 29 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1545 https://www.mathnet.ru/rus/sigma/v16/p8
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