Geodesic
Cones of traces arising from AF $C^{*}$-algebras
Documenta mathematica, Tome 28 (2023) no. 6, pp. 1279-1321

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We characterize the topological non-cancellative cones that can be expressed as projective limits of finite powers of [0,∞]. For metrizable cones, these are also the cones of lower semicontinuous extended-valued traces on approximately finite-dimensional (AF) C∗-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.
DOI : 10.4171/dm/927
Classification : 06F30, 06B30, 46A55, 46L05
Mots-clés : non-cancellative cones, projective limit, AF C∗-algebras 
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Mark Moodie; Leonel Robert. Cones of traces arising from AF $C^{*}$-algebras. Documenta mathematica, Tome 28 (2023) no. 6, pp. 1279-1321. doi: 10.4171/dm/927

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