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- W3157036857 abstract "Suppose $D$ is a finite dimensional C*-algebra carrying a continuous action $overline{Pi}$ of the circle group $mathbb{T}$. We study the quantum symmetry group of $D$, taking $overline{Pi}$ into account. We show that they are braided compact quantum groups $mathbb{G}$ over $mathbb{T}$. Here, the R-matrix, $mathbb{Z}timesmathbb{Z}ni (m,n)to zeta^{-mcdot n}inmathbb{T}$ for a fixed $zetain mathbb{T}$, governs the braided structure. In particular, if $overline{Pi}$ is trivial, $zeta=1$ or $D$ is commutative, then $mathbb{G}$ coincides with Wang's quantum group of automorphisms of $D$. Moreover, we show that the bosonisation of $mathbb{G}$ corresponds to the quantum symmetry group of the crossed product C*-algebra $Drtimesmathbb{Z}$, where the $mathbb{Z}$-action is generated by $overline{Pi}_{zeta{^{-1}}}$." @default.
- W3157036857 created "2021-05-10" @default.
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- W3157036857 date "2021-05-04" @default.
- W3157036857 modified "2023-09-27" @default.
- W3157036857 title "Homogeneous quantum symmetries of finite spaces over the circle group" @default.
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