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- W4313854769 abstract "Let $B$ be a finite dimensional C$^ast$-algebra equipped with its canonical trace induced by the regular representation of $B$ on itself. In this paper, we study various properties of the trace-preserving quantum automorphism group $G$ of $B$. We prove that the discrete dual quantum group $hG$ has the property of rapid decay, the reduced von Neumann algebra $L^infty(G)$ has the Haagerup property and is solid, and that $L^infty(G)$ is (in most cases) a prime type II$_1$-factor. As applications of these and other results, we deduce the metric approximation property, exactness, simplicity and uniqueness of trace for the reduced $C^ast$-algebra $C_r(G)$, and the existence of a multiplier-bounded approximate identity for the convolution algebra $L^1(G)$." @default.
- W4313854769 created "2023-01-10" @default.
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- W4313854769 date "2012-02-22" @default.
- W4313854769 modified "2023-09-30" @default.
- W4313854769 title "Reduced operator algebras of trace-preserving quantum automorphism groups" @default.
- W4313854769 doi "https://doi.org/10.48550/arxiv.1202.5020" @default.
- W4313854769 hasPublicationYear "2012" @default.
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