Equivariant higher Dixmier-Douady theory for UHF-algebras

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• Valerio Bianchi (Cardiff University)
• Thursday 03 July 2025, 15:30-15:50
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TGAW01 - Crossed products and groupoid C*-algebras

A classical result of Dixmier and Douady enables us to classify locally trivial bundles of C-algebras with compact operators as fibres via methods in homotopy theory. Dadarlat and Pennig have shown that this generalises to the much larger family of bundles of stabilised strongly self-absorbing C-algebras, which are classified by the first group of the cohomology theory associated to the units of complex topological K-theory. Building on work of Evans and Pennig I consider Z/pZ-equivariant C-algebra bundles over Z/pZ-spaces. The fibres of these bundles are infinite tensor products of the endomorphism algebra of a Z/pZ-representation. In joint work with Pennig we show that the theory refines completely to this equivariant setting. In particular, we prove a full classification of the C-algebra bundles via equivariant stable homotopy theory.

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

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