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arXiv · 1804.07032

Principal fibrations over noncommutative spheres

Michel Dubois-Violette·Xiao Han·Giovanni Landi
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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.

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Michel Dubois-Violette, Xiao Han, Giovanni Landi. 2018-04-19. Principal fibrations over noncommutative spheres. https://doi.org/10.1142/s0129055x18500204

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