Faithful actions of locally compact quantum groups on classical spaces

Faithful actions of locally compact quantum groups on classical spaces We construct examples of locally compact quantum groups coming from bicrossed product construction, including non-Kac ones, which can faithfully and ergodically act on connected classical (noncompact) smooth manifolds. However, none of these actions can be isometric in the sense of Goswami (Commun Math Phys 285(1):141–160, 2009), leading to the conjecture that the result obtained by Goswami and Joardar (Rigidity of action of compact quantum groups on compact, connected manifolds, 2013. arXiv:1309.1294 ) about nonexistence of genuine quantum isometry of classical compact connected Riemannian manifolds may hold in the noncompact case as well. Letters in Mathematical Physics Springer Journals

Faithful actions of locally compact quantum groups on classical spaces

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Springer Netherlands
Copyright © 2017 by Springer Science+Business Media Dordrecht
Physics; Theoretical, Mathematical and Computational Physics; Complex Systems; Geometry; Group Theory and Generalizations
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