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Version: publishedVersion × Publisher: Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach × Subject: automorphism ×

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Now showing 1 - 3 of 3
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    Localized endomorphisms of graph algebras
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Conti, Roberto; Hong, Jeong Hee; Szyma´nski, Wojciech
    Endomorphisms of graph C*-algebras are investigated. A combinatorial ap- proach to analysis of permutative endomorphisms is developed. Then invertibility criteria for localized endomorphisms are given. Furthermore, proper endomor- phisms which restrict to automorphisms of the canonical diagonal MASA are analyzed. The Weyl group and the restricted Weyl group of a graph C*-algebra are introduced and investigated. Criteria of outerness for automorphisms in the restricted Weyl group are found.
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    The Weyl group of the Cuntz algebra
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Conti, Roberto; Hong, Jeong Hee; Szyma´nski, Wojciech
    The Weyl group of the Cuntz algebra On is investigated. This is (isomorphic to) the group of polynomial automorphisms λu of On, namely those induced by unitaries u that can be written as finite sums of words in the canonical generating isometries Si and their adjoints. A necessary and sufficient algorithmic combinatorial condition is found for deciding when a polynomial endomorphism λu restricts to an automorphism of the canonical diagonal MASA. Some steps towards a general criterion for invertibility of λu on the whole of On are also taken. A condition for verifying invertibility of a certain subclass of polynomial endomorphisms is given. First examples of polynomial automorphisms of On not inner related to permutative ones are exhibited, for every n≥2. In particular, the image of the Weyl group in the outer automorphism group of On is strictly larger than the image of the reduced Weyl group analyzed in previous papers. Results about the action of the Weyl group on the spectrum of the diagonal are also included.
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    On conjugacy of MASAs and the outer automorphism aroup of the Cuntz algebra
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2013) Conti, Roberto; Hong, Jeong Hee; Szyma´nski, Wojciech
    We investigate the structure of the outer automorphism group of the Cuntz algebra and the closely related problem of conjugacy of MASAa in On. In particular, we exhibit an uncountable family of MASAs, conjugate to the standard MASA Dn via Bogolubov automorphisms, that are not inner conjugate to Dn.