Quantum symmetries of classical spaces

Abstract

We give a general scheme for constructing faithful actions of genuine (noncommutative as $C^{\ast }$ 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.

This paper is withdrawn due to a gap in the main construction

References in corpus (1)

• Quantum Group of Orientation preserving Riemannian Isometries