Quantum symmetries of classical spaces

Details Quantum symmetries of classical spaces Quantum symmetries of classical spaces

2009-03-07

arxiv.org/abs/0903.1322v3

Mathematics

Quantum Algebra

This paper is withdrawn due to a gap in the main construction

Scientific paper

We give a general scheme for constructing faithful actions of genuine (noncommutative as $C^*$ algebra) compact quantum groups on classical topological spaces. Using this, we show that: (i) a compact connected classical space can have a faithful action by a genuine compact quantum group, and (ii) there exists a spectral triple on a classical connected compact space for which the quantum group of orientation and volume preserving isometries (in the sense of \cite{qorient}) is a genuine quantum group.

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