Principal groupoid models for the Cuntz algebras

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• Samuel Evington (Westfalische Wilhelms-Universitat Munster)
• Thursday 17 July 2025, 10:25-10:45
• External.

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TGAW02 - C*-algebras: classification and dynamical constructions

I will begin with a brief discussion of Renault’s classical construction of a groupoid that gives rise to the Cuntz algebra O_n with its canonical Cartan subalgebra. Renault’s groupoid model has isotropy (i.e. the dynamics has some fixed points). This means that the canonical Cartan in O_n isn’t a C-diagonal, and in particular has infinite diagonal dimension.   In the second half of the talk, I will outline my recent work with Philipp Sibbel on constructing a groupoid model for the Cuntz algebra O_n with no isotropy (i.e. a principal groupoid). This groupoid gives rise to a C-diagonal inside of O_n whose spectrum is a Cantor space.   The groupoid can be realised as a product of the Deaconu-Renault groupoid associated to a well-chosen topological graph with the groupoid of a well-chosen AF equivalence relation.

This talk is part of the Isaac Newton Institute Seminar Series series.

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