L. I. Vainerman
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Methods Funct. Anal. Topology 23 (2017), no. 1, 76-107
We study coactions of finite quantum groupoids on unital $C^*$-algebras and obtain a Tannaka-Krein reconstruction theorem for them.
Methods Funct. Anal. Topology 21 (2015), no. 3, 282-298
The last decade saw an appearance of a series of papers containing a very interesting development of the Tannaka-Krein duality for compact quantum group coactions on $C^*$-algebras. The present survey is intended to present the main ideas and constructions underlying this development.
Methods Funct. Anal. Topology 14 (2008), no. 2, 102-107