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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• Guihua Gong
University of Puerto Rico
Classification of inductive limit C*-algebras with ideal property
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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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• David Kerr
Texas A&M University
Sin título
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• Maria Grazia Viola
Lakehead University
Structure of ideals in a spatial $L^p$ AF algebra
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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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