Geodesic
Reduced operator algebras of trace-preserving quantum automorphism groups
Documenta mathematica, Tome 18 (2013), pp. 1349-1402
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Let B be a finite dimensional C∗-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 G has the property of rapid decay, the reduced von Neumann algebra L∞(G) has the Haagerup property and is solid, and that L∞(G) is (in most cases) a prime type II1​-factor. As applications of these and other results, we deduce the metric approximation property, exactness, simplicity and uniqueness of trace for the reduced C∗-algebra Cr​(G), and the existence of a multiplier-bounded approximate identity for the convolution algebra L1(G).
DOI : 10.4171/dm/430
Classification : 20G42, 46L54, 46L65
Mots-clés : quantum automorphism groups, approximation properties, property of rapid decay, II_1-factor, solid von Neumann algebra, temperley-Lieb algebra 
@article{10_4171_dm_430,
     author = {Michael Brannan},
     title = {Reduced operator algebras of trace-preserving quantum automorphism groups},
     journal = {Documenta mathematica},
     pages = {1349--1402},
     year = {2013},
     volume = {18},
     doi = {10.4171/dm/430},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/430/}
}
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Michael Brannan. Reduced operator algebras of trace-preserving quantum automorphism groups. Documenta mathematica, Tome 18 (2013), pp. 1349-1402. doi: 10.4171/dm/430

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