Reduced operator algebras of trace-preserving quantum automorphism groups
Michael BrannanDepartment of Mathematics University of Illinois Urbana, IL 61801 USA
Let be a finite dimensional C-algebra equipped with its canonical trace induced by the regular representation of on itself. In this paper, we study various properties of the trace-preserving quantum automorphism group of . We prove that the discrete dual quantum group has the property of rapid decay, the reduced von Neumann algebra has the Haagerup property and is solid, and that is (in most cases) a prime type II-factor. As applications of these and other results, we deduce the metric approximation property, exactness, simplicity and uniqueness of trace for the reduced -algebra , and the existence of a multiplier-bounded approximate identity for the convolution algebra .
Cite this article
Michael Brannan, Reduced operator algebras of trace-preserving quantum automorphism groups. Doc. Math. 18 (2013), pp. 1349–1402DOI 10.4171/DM/430