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Hiroki Matui

  1. Classification of homomorphisms into simple Z-stable C^*-algebras.

    Пт, 02/26/2010 - 16:01 — SomNambul
    Authors: Hiroki Matui
    Subjects: Operator Algebras
    Abstract

    We classify unital monomorphisms into certain simple Z-stable C^*-algebras up
    to approximately unitarily equivalence. The domain algebra C is allowed to be
    any unital separable commutative C^*-algebra, or any unital simple separable
    nuclear Z-stable C^*-algebra satisfying the UCT such that C\otimes B is of
    tracial rank zero for a UHF algebra B.

  2. Z-stability of crossed products by strongly outer actions.

    Пт, 12/25/2009 - 16:01 — SomNambul
    Authors: Hiroki Matui, Yasuhiko Sato
    Subjects: Operator Algebras
    Abstract

    We consider a certain class of unital simple stably finite C^*-algebras which
    absorb the Jiang-Su algebra Z tensorially. Under a mild assumption, we show
    that the crossed product of a C^*-algebra in this class by a strongly outer
    action of Z^N or a finite group is Z-stable. As an application, we also prove
    that any strongly outer actions of Z^2 on Z are mutually cocycle conjugate.

  3. Homology and topological full groups of etale groupoids on totally disconnected spaces.

    Чт, 09/10/2009 - 10:12 — SomNambul
    Authors: Hiroki Matui
    Subjects: Operator Algebras
    Abstract

    For almost finite groupoids, we study how their homology groups reflect
    dynamical properties of their topological full groups. It is shown that two
    clopen subsets of the unit space has the same class in H_0 if and only if there
    exists an element in the topological full group which maps one to the other. It
    is also shown that a natural homomorphism, called the index map, from the
    topological full group to H_1 is surjective and any element of the kernel can
    be written as a product of four elements of finite order.

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