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Nathan Brownlowe

  1. Co-universal C*-algebras associated to generalised graphs.

    Wed, 09/08/2010 - 15:01 — SomNambul
    Authors: Nathan Brownlowe, Sean T. Vittadello, Aidan Sims
    Subjects: Operator Algebras
    Abstract

    We introduce P-graphs, which are generalisations of directed graphs in which
    paths have a degree in a semigroup P rather than a length in N. We focus on
    semigroups P arising as part of a quasi-lattice ordered group (G,P) in the
    sense of Nica, and on P-graphs which are finitely aligned in the sense of
    Raeburn and Sims. We show that each finitely aligned P-graph admits a
    C*-algebra C*_{min}(Lambda) which is co-universal for partial-isometric
    representations of Lambda which admit a coaction of G compatible with the
    P-valued length function.

  2. Realising the C*-algebra of a higher-rank graph as an Exel crossed product.

    Thu, 12/24/2009 - 16:01 — SomNambul
    Authors: Nathan Brownlowe
    Subjects: Operator Algebras
    Abstract

    We use the boundary-path space of a finitely-aligned k-graph \Lambda to
    construct a compactly-aligned product system X, and we show that the graph
    algebra C^*(\Lambda) is isomorphic to the Cuntz-Nica-Pimsner algebra NO(X). In
    this setting, we introduce the notion of a crossed product by a semigroup of
    partial endomorphisms and partially-defined transfer operators by defining it
    to be NO(X). We then compare this crossed product with other definitions in the
    literature.

  3. Exel's crossed product for non-unital C*-algebras.

    Thu, 08/20/2009 - 23:06 — SomNambul
    Authors: Nathan Brownlowe, Iain Raeburn, Sean T. Vittadello
    Subjects: Operator Algebras
    Abstract

    We consider a family of dynamical systems (A,alpha,L) in which alpha is an
    endomorphism of a C*-algebra A and L is a transfer operator for \alpha. We
    extend Exel's construction of a crossed product to cover non-unital algebras A,
    and show that the C*-algebra of a locally finite graph can be realised as one
    of these crossed products. When A is commutative, we find criteria for the
    simplicity of the crossed product, and analyse the ideal structure of the
    crossed product.

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