Geodesic
Reduced operator algebras of trace-preserving quantum automorphism groups
Documenta mathematica, Tome 18 (2013), pp. 1349-1402.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $L^1(\G)$.
Classification : 46L65, 20G42, 46L54
Keywords: quantum automorphism groups, approximation properties, property of rapid decay, II_1-factor, solid von Neumann algebra, temperley-Lieb algebra 
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     author = {Brannan, Michael},
     title = {Reduced operator algebras of trace-preserving quantum automorphism groups},
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     year = {2013},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a8/}
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Brannan, Michael. Reduced operator algebras of trace-preserving quantum automorphism groups. Documenta mathematica, Tome 18 (2013), pp. 1349-1402. http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a8/