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{\Large Department of Mathematics, BGU}

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{\Huge Operator Algebras and Operator Theory}\\[0.2\baselineskip]

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\textbf{On} \emph{Monday, December 25, 2017}
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\textbf{At} \emph{16:00 -- 17:00}
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\textbf{In} \emph{-101}

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{\large\scshape Adam Dor-On 
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will talk about
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{\Large\bfseries Representations of Toeplitz-Cuntz-Krieger algebras\par}
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\textsc{Abstract:}
By a result of Glimm, we know that classifying
representations of non-type-I $C^*$-algebras up to unitary equivalence is essentially impossible (at least with countable structures). Instead of this, one either restricts to a tractable subclass or weakens the invariant.

In the theory of free semigroup algebras, the latter is done for Toeplitz-Cuntz algebras, and is achieved via two key results in the theory: the first is a theorem of Davidson, Katsoulis and Pitts on the $2\times 2$ structure of free semigroup algebras, and the second, a Lebesuge-von Neumann-Wold decomposition theorem of Kennedy.

This talk is about joint work with Ken Davidson and Boyu Li, where we generalize this theory to representations of Toeplitz-Cuntz-\emph{Krieger} algebras associated to a directed graph $G.$ We prove a structure theorem akin to that of Davidson, Katsoulis and Pitts, and provide a Lebesuge-von Neumann Wold decomposition using Kennedy's theorem. We discuss some of the difficulties and similarities when passing to the more general context of operator algebras associated to directed graphs.








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