Mathematische Annalen

, Volume 314, Issue 4, pp 763–780 | Cite as

Symmetries of a generic coaction

  • Teodor Banica


If B is \({\bf C}^*\)-algebra of dimension $4\leq n<\infty$ then the finite dimensional irreducible representations of the compact quantum automorphism group of B, say \(G_{aut}(\widehat{B})\), have the same fusion rules as the ones of SO(3). As consequences, we get (1) a structure result for \(G_{aut}(\widehat{B})\) in the case where B is a matrix algebra (2) if \(n\geq 5\) then the dual \(\widehat{G}_{aut}(\widehat{B})\) is not amenable (3) if \(n\geq 4\) then the fixed point subfactor \(P^{G_{aut}(\widehat{B})}\subset (B\otimes P)^{G_{aut}(\widehat{B})}\) has index n and principal graph \(A_\infty\).

Mathematics Subject Classification (1991):81R50, 46L37 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Teodor Banica
    • 1
  1. 1. Institut de Mathématiques de Jussieu, Case 191, Université Paris 6, 4 Place Jussieu, F-75005 Paris, France (e-mail: FR

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