Categorical models for ample groupoids and their algebras

Abstract: A decade ago, Spielberg described a new method for defining $C^*$-algebras from oriented combinatorial data, generalizing the construction of algebras from directed graphs, higher-rank graphs, and (quasi-)ordered groups. To do so, he introduced left cancellative small categories, and endowed any such category with a $C^*$-algebra encoding categorical information; he showed that this algebra is the groupoid algebra of a (sort of) Deaconu-Renault étale groupoid.

"In this talk, we explain the relevance of these algebras. Furthermore, we show that they are Exel's groupoid $C^*$-algebras associated to a suitable inverse semigroup $\mathcal{S}_\Lambda$; this would allow us characterize their properties, like being Hausdorff, effective and minimal, and thus simplicity for these algebras. We the study groupoid actions on left cancellative small categories and their associated Zappa-Szép products, by reducing them to Spielberg's model.

The contents of this talk are joint work with Eduard Ortega (NTNU Trondheim, Norway)."

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( slides | video )

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Noncommutative geometry in NYC

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