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Search: MSC category 46L65 ( Quantizations, deformations )

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1. CJM 2016 (vol 68 pp. 698)

 Quantum Families of Invertible Maps and Related Problems The notion of families of quantum invertible maps (C$^*$-algebra homomorphisms satisfying PodleÅ' condition) is employed to strengthen and reinterpret several results concerning universal quantum groups acting on finite quantum spaces. In particular Wang's quantum automorphism groups are shown to be universal with respect to quantum families of invertible maps. Further the construction of the Hopf image of Banica and Bichon is phrased in the purely analytic language and employed to define the quantum subgroup generated by a family of quantum subgroups or more generally a family of quantum invertible maps. Keywords:quantum families of invertible maps, Hopf image, universal quantum groupCategories:46L89, 46L65
 On Amenability and Co-Amenability of Algebraic Quantum Groups and Their Corepresentations We introduce and study several notions of amenability for unitary corepresentations and $*$-representations of algebraic quantum groups, which may be used to characterize amenability and co-amenability for such quantum groups. As a background for this study, we investigate the associated tensor C$^{*}$-categories. Keywords:quantum group, amenabilityCategories:46L05, 46L65, 22D10, 22D25, 43A07, 43A65, 58B32