Symmetries of a generic coaction

Details Symmetries of a generic coaction Symmetries of a generic coaction

1998-11-09

arxiv.org/abs/math/9811060v2

Math. Ann. 314 (1999), 763-780

Mathematics

Quantum Algebra

12 pages, amslatex. v2 contains detailed proofs of the 3 corollaries, to appear in Math. Ann

Scientific paper

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.

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