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- W2963410590 abstract "We formulate a definition of isometric action of a compact quantum group (CQG) on a compact metric space, generalizing Banica's definition for finite metric spaces. For metric spaces (X,d) which can be isometrically embedded in some Euclidean space, we prove the existence of a universal object in the category of the compact quantum groups acting isometrically on (X,d). In fact, our existence theorem applies to a larger class, namely for any compact metric space (X,d) which admits a one-to-one continuous map f:X→Rn for some n such that d0(f(x),f(y))=ϕ(d(x,y)) (where d0 is the Euclidean metric) for some homeomorphism ϕ of R+. As concrete examples, we obtain Wang's quantum permutation group Sn+ and also the free wreath product of Z2 by Sn+ as the quantum isometry groups for certain compact connected metric spaces constructed by taking topological joins of intervals in [13]." @default.
- W2963410590 created "2019-07-30" @default.
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- W2963410590 date "2015-08-01" @default.
- W2963410590 modified "2023-09-23" @default.
- W2963410590 title "Existence and examples of quantum isometry groups for a class of compact metric spaces" @default.
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- W2963410590 doi "https://doi.org/10.1016/j.aim.2015.03.024" @default.
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