Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 062, 19 pages      arXiv:1701.05895      https://doi.org/10.3842/SIGMA.2017.062

Part III, Free Actions of Compact Quantum Groups on ${\rm C}^*$-Algebras

Kay Schwieger a and Stefan Wagner b
a) Iteratec GmbH, Stuttgart, Germany
b) Blekinge Tekniska Högskola, Sweden

Received April 05, 2017, in final form August 05, 2017; Published online August 09, 2017

Abstract
We study and classify free actions of compact quantum groups on unital ${\rm C}^*$-algebras in terms of generalized factor systems. Moreover, we use these factor systems to show that all finite coverings of irrational rotation ${\rm C}^*$-algebras are cleft.

Key words: free action; ${\rm C}^*$-algebra; quantum group; factor system; finite covering.

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