Symmetries of a generic coaction

1998/11/30 by Teodor Banica
Mathematics · #math.QA

paper · pdf

published as Math. Ann. 314 (1999), 763-780 · 12 pages, amslatex. v2 contains detailed proofs of the 3 corollaries, to appear in Math. Ann

arxiv created 1999/01/29 · arxiv updated 2009/11/30

Abstract

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⊂ (B⊗ P)^G has index n and principal graph A_∞.

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