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Efren Ruiz

  1. Classifying $C^*$-algebras with both finite and infinite subquotients.

    Пнд, 09/27/2010 - 15:01 — SomNambul
    Authors: Efren Ruiz, Soren Eilers, Gunnar Restorff
    Subjects: Operator Algebras
    Abstract

    We give a classification result for a certain class of $C^{*}$-algebras
    $\mathfrak{A}$ over a finite topological space $X$ in which there exists an
    open set $U$ of $X$ such that $U$ separates the finite and infinite
    subquotients of $\mathfrak{A}$. We will apply our results to $C^{*}$-algebras
    arising from graphs.

  2. Axiomatic $KK$-theory for Real C*-algebras.

    Втр, 09/08/2009 - 12:16 — SomNambul
    Authors: Jeffrey L. Boersema, Efren Ruiz
    Subjects: Operator Algebras
    Abstract

    We establish axiomatic characterizations of $K$-theory and $KK$-theory for
    real C*-algebras. In particular, let $F$ be an abelian group-valued functor on
    separable real C*-algebras. We prove that if $F$ is homotopy invariant, stable,
    and split exact, then $F$ factors through the category $KK$. Also, if $F$ is
    homotopy invariant, stable, half exact, continuous, and satisfies an
    appropriate dimension axiom, then there is a natural isomorphism $K(A) \to
    F(A)$ for a large class of separable real C*-algebras $A$.

  3. Axiomatic $KK$-theory for Real C*-algebras.

    Втр, 09/08/2009 - 12:16 — SomNambul
    Authors: Jeffrey L. Boersema, Efren Ruiz
    Subjects: Operator Algebras
    Abstract

    We establish axiomatic characterizations of $K$-theory and $KK$-theory for
    real C*-algebras. In particular, let $F$ be an abelian group-valued functor on
    separable real C*-algebras. We prove that if $F$ is homotopy invariant, stable,
    and split exact, then $F$ factors through the category $KK$. Also, if $F$ is
    homotopy invariant, stable, half exact, continuous, and satisfies an
    appropriate dimension axiom, then there is a natural isomorphism $K(A) \to
    F(A)$ for a large class of separable real C*-algebras $A$.

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