Classification of simple $C^*$-algebras from singular graphs

Soren Eilers  (University of Copenhagen)

11:00-12:00£¨July 30th£¨2024    Tian Jiabing Building 323




Abstract:

There is a rich classification theory for unital simple $C^*$-algebras associated to finite graphs with no sinks, allowing to decide by invariants when two such $C^*$-algebras are isomorphic, not just in their own right, but equipped with their natural diagonals (Cartan subalgebras) or their natural circle actions. All of these results were proved by involving results from symbolic dynamics, even though some now are special cases of much more general results. When one allows singular vertices-sinks or infinite emitters-the connection to the rich theory of shifts of finite type is lost, but the classical classification results have natural generalizations which one may aspire to show by other means. I will discuss and compare different notions of sameness of such graph $C^*$-algebras; all fully understood in the regular case, buth only half resolved in general. All work presented is joint with Efren Ruiz, and some also with Aidan Sims.

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