Cones of traces arising from AF -algebras
M. Moodie
San Jacinto College, Houston, USAL. Robert
University of Louisiana at Lafayette, USA
![Cones of traces arising from AF $C^{*}$-algebras cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-dm-volume-28-issue-6.png&w=3840&q=90)
Abstract
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.
Cite this article
M. Moodie, L. Robert, Cones of traces arising from AF -algebras. Doc. Math. 28 (2023), no. 6, pp. 1279–1321
DOI 10.4171/DM/927