Classification of Amenable C*-algebras

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Organizers:
  • George Elliott (University of Toronto)
  • Benjamin Itza-Ortiz (Autonomous University of Hidalgo)
  • Fernando Mortari (UFSC)
  • Zhuang Niu (University of Wyoming)
    • Huaxin Lin
      University of Oregon
    Recent results in the Elliott program
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    We will discuss recent progresses in the Elliott program of classification of simple amenable C*-algebras, including non-unital cases
    • Bhishan Jacelon
      University of Toronto
    Sin título
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    Size: 25 kb
    • Guihua Gong
      University of Puerto Rico
    Classification of inductive limit C*-algebras with ideal property
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    Size: 53 kb
    A C*-algebra is said to have ideal property if each of its ideal is generated by projections inside the ideal. This class of C*-algebras is a common generalization of unital simple C*algebras and real rank zero C*-algebras. In this talk, we will present a classification of AH algebras with ideal property. The invariant involves scaled ordered total K-theory, tracial state spaces of cutting down algebras and new ingredient of Hausdorffized algebraic $K_1$ of cutting down algebras with certain compatibility. The talk is based on two joint papers of Gong-Jiang-Li-Pasnicu and Gong-Jiang-Li.
    • Liangqing Li
      University of Puerto Rico
    Exponential length of commutator unitaries of simple AH C*-algebras.
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    Abstract: Let $A$ be a unital $C^*$-algebra, and let $CU(A)$ denote the closure of the set of all commutators of the unitary group of $A$. Let $cel_{CU}(A)$ denote supremum of exponential lengths of all $u\in CU(A)$. Huaxin Lin proved that if $A$ is a TAI algebra, then $cel_{CU}(A)\leq 2\pi$. Lin also proved that for each countable ordered weakly unperforated Riesz group $(G, G_+)$ and each countable group $H$, there is a simple AH algebra of tracial rank one such that $(K_0(A), K_0(A)_+, K_1(A))= (G, G_+, H) $ and $cel_{CU}(A)>\pi$. In this talk, I will present the following theorem: for any simple AH algebra $A$ of traicial rank one, $cel_{CU}(A)=2\pi$. This is a joint work with Chunguang Li and Ivan Valesques.
    • Ping Wong Ng
      University of Luisiana at Lafayette
    Sin título
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    • Andrew Dean
      Lakehead University
    Classification Problems Involving Real C*-algebras
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    We shall discuss results on classifying categories of real C*-algebras and actions on them using K-theoretic invariants.
    • Viviane Beuter
      Federal University of Santa Catarina (UFSC)
    Simplicity of skew inverse semigroup rings with an application to Steinberg algebras
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    Given an action $\alpha$ of an inverse semigroup $\mathcal{S}$ on a associative ring $\mathcal{A}$ one may construct its associated skew inverse semigroup ring $\mathcal{A} \rtimes_\alpha \mathcal{S}$. We assume that $\mathcal{A}$ is commutative and we define a certain commutative subring $\mathcal{T}$ of $\mathcal{A} \rtimes_\alpha S$ which coincides with the embedding of $\mathcal{A}$ in $\mathcal{A} \rtimes_\alpha S$ whenever $S$ is unital. Our main result asserts that $\mathcal{A} \rtimes_\alpha S$ is a simple ring if, and only if, $\mathcal{T}$ is a maximal commutative subring of $\mathcal{A} \rtimes_\alpha S$ and $\mathcal{A}$ is $\mathcal{S}$-simple. As an application of our result we present a new proof of the simplicity criterion for a Steinberg algebra $A_R(\mathcal{G})$ associated with a Hausdorff and ample groupoid $\mathcal{G}$.
    • N. Christopher Phillips
      University of Oregon
    Sin título
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    Size: 26 kb
    • David Kerr
      Texas A&M University
    Sin título
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    Size: 25 kb
    • Maria Grazia Viola
      Lakehead University
    Structure of ideals in a spatial $L^p$ AF algebra
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    Size: 59 kb
    Spatial $L^p$ AF algebras were introduced by Phillips and Viola, and shown to be completely classifiable by their scaled preordered $K_0$ group. In this talk we describe the structure of ideals of a spatial $L^p$ AF algebra. We also show that any spatial $L^p$ AF algebra is residually incompressible and completely residually incompressible. We conclude by discussing some properties of the automorphisms of a spatial $L^p$ AF algebras.
    • Leonel Robert
      University of Louisiana at Lafayette
    Dixmier sets of C*-algebras
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    I call "Dixmier set" a closed convex subset of a C*-algebra that is invariant under unitary conjugation. Similar sets can be defined in the dual of a C*-algebra (now using the weak* topology). I will talk about several natural questions on these sets and the answers that we know. Some of this work is joint with Ng and Skoufranis, some joint with Archbold and Tikuisis, some is still in progress.
    • Luis Santiago
      Lakehead University
    Sin título
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    Size: 25 kb