On actions of compact quantum groups. (English) Zbl 1272.46054

Summary: We compare algebraic objects related to a compact quantum group action on a unital \(C^\ast\)-algebra in the sense of P. Podleś and P. Baum et al. and show that they differ by the kernel of the morphism describing the action. Then we address ways to remove the kernel without changing the Podleś algebraic core. Such a minimal procedure is described. We end the paper with a natural example of an action of a reduced compact quantum group with nontrivial kernel.


46L65 Quantizations, deformations for selfadjoint operator algebras
17B37 Quantum groups (quantized enveloping algebras) and related deformations
20G42 Quantum groups (quantized function algebras) and their representations
81R60 Noncommutative geometry in quantum theory


Zbl 0853.46074
Full Text: arXiv Euclid


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