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The structure of the automorphism group of an approximately finite dimensional factor. (English) Zbl 1021.46043
Longo, Roberto (ed.), Mathematical physics in mathematics and physics. Quantum and operator algebraic aspects. Proceedings of a conference, Siena, Italy, June 20-24, 2000. Dedicated to Sergio Doplicher and John E. Roberts on the occasion of their 60th birthday. Providence, RI: AMS, American Mathematical Society. Fields Inst. Commun. 30, 249-260 (2001).
Summary: The present notes are concerned with the automorphism group \(\operatorname{Aut}({\mathcal R})\) of an approximately finite dimensional, to be abbreviated by AFD, factor \({\mathcal R}\). We point out a surprising fact about an AFD factor, namely that the quotient map of \(\operatorname{Aut}({\mathcal R})\) by \(\overline{\text{Int}}({\mathcal R})\), which is the kernel of the modulus map, admits a right inverse for an AFD factor \({\mathcal R}\). In this article, we investigate the detailed structure of the automorphism group \(\operatorname{Aut}({\mathcal R})\).
For the entire collection see [Zbl 0979.00039].

46L35 Classifications of \(C^*\)-algebras
46L40 Automorphisms of selfadjoint operator algebras
22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations