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arXiv · 2009.09033

Cones of traces arising from AF C*-algebras

Mark Moodie·Leonel Robert
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Abstract

We characterize the topological non-cancellative cones that are expressible as projective limits of finite powers of $[0,\infty]$. These are also the cones of lower semicontinuous extended-valued traces on 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.

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Mark Moodie, Leonel Robert. 2020-09-18. Cones of traces arising from AF C*-algebras. https://arxiv.org/abs/2009.09033

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