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Principal fibrations over noncommutative spheres

TitlePrincipal fibrations over noncommutative spheres
Publication TypeJournal Article
Year of Publication2018
AuthorsDubois-Violette, M, Han, X, Landi, G
JournalReviews in Mathematical Physics
Volume30
Pagination1850020
Abstract

We present examples of noncommutative four-spheres that are base spaces of $SU(2)$-principal bundles with noncommutative seven-spheres as total spaces. The noncommutative coordinate algebras of the four-spheres are generated by the entries of a projection which is invariant under the action of $SU(2)$. We give conditions for the components of the Connes–Chern character of the projection to vanish but the second (the top) one. The latter is then a non-zero Hochschild cycle that plays the role of the volume form for the noncommutative four-spheres.

URLhttps://arxiv.org/abs/1804.07032
DOI10.1142/S0129055X18500204

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