Symmetries of a generic coaction
Abstract
Description
If B is C*-algebra of finite dimension n>3 then the finite dimensional irreducible representations of the compact quantum automorphism group of B, say G, have the same fusion rules as the ones of SO(3). As consequences, we get (1) a structure result for G in the case where B is a matrix algebra (2) if n>4 then the dual of G is not amenable (3) the fixed point subfactor P^G\subset (B\otimes P)^G has index n and principal graph A_\infty.
12 pages, amslatex. v2 contains detailed proofs of the 3 corollaries, to appear in Math. Ann
12 pages, amslatex. v2 contains detailed proofs of the 3 corollaries, to appear in Math. Ann