Ample groupoids and C*-algebras from rings of algebraic integers: rigidity and homology

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• Chris Bruce (Newcastle University)
• Thursday 03 July 2025, 09:00-10:00
• External.

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TGAW01 - Crossed products and groupoid C*-algebras

Each ring of algebraic integers in a number field gives rise to an ample (étale) groupoid and a corresponding groupoid C-algebra. I will present on joint work with Xin Li in which we prove several rigidity theorems for this construction, showing that the groupoid (equivalently, the associated Cartan pair of C-algebras) completely remembers the ring. I will also present on joint work with Yosuke Kubota and Takuya Takeishi where we compute groupoid homology for our groupoids. These homology computations combined with a recent breakthrough by Xin Li lead to simplicity results for the topological full groups attached to rings of algebraic integers.

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

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