On the quantum twistor bundle

Abstract: The concept of a quantum principal bundle is well established by now. However, general (locally trivial) fiber bundles are much less understood in the noncommutative setting. We investigate a noncommutative sphere bundle from what we call the quantum twistor bundle.It is constructed as a quotient of the quantum instanton bundle of Bonechi, Ciccoli and Tarlini $SU_q(2)\to S_q^7\to S_q^4$ for a suitable circle action on the Vaksmann-Soibelman quantum sphere $S_q^7$. It is an example of a locally trivial noncommutative bundle fulfilling conditions of the framework proposed by Brzeziski and Szymanski.

functional analysisgroup theoryoperator algebrasquantum algebra

Audience: researchers in the topic

Groups, Operators, and Banach Algebras Webinar

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