Cones of traces arising from AF -algebras

  • M. Moodie

    San Jacinto College, Houston, USA
  • L. Robert

    University of Louisiana at Lafayette, USA
Cones of traces arising from AF $C^{*}$-algebras cover
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We characterize the topological non-cancellative cones that can be expressed as projective limits of finite powers of . For metrizable cones, these are also the cones of lower semicontinuous extended-valued traces on approximately finite-dimensional (AF) -algebras. Our main result may be regarded as a generalization of the fact that any Choquet simplex is a projective limit of finite-dimensional simplices. To obtain our main result, we first establish a duality between certain non-cancellative topological cones and Cuntz semigroups with real multiplication. This duality extends the duality between compact convex sets and complete order unit vector spaces to a non-cancellative setting.

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M. Moodie, L. Robert, Cones of traces arising from AF -algebras. DM 28 (2023), no. 6, pp. 1279–1321

DOI 10.4171/DM/927