Good traces for not necessarily simple dimension groups

DOI10.2140/PJM.2016.281.365zbMATH Open1354.37018arXiv1309.7424OpenAlexW1668462598MaRDI QIDQ5962784

Publication date: 24 February 2016

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Abstract: Akin's notion of good measure, introduced to classify measures on Cantor sets has been translated to dimension groups and corresponding traces by Bezuglyi and the author, but emphasizing the simple (minimal dynamical system) case. Here we deal with non-simple (non-minimal) dimension groups. In particular, goodness of tensor products of large classes of non-good traces (measures) is established. We also determine the pure faithful traces on the dimension groups associated to xerox type actions on AF C*-algebras; the criteria turn out to involve algebraic geometry and number theory. We also deal with a coproduct of dimension groups, wherein, despite expectations, goodness of direct sums is nontrivial. In addition, we verify a conjecture of [BeH] concerning good subsets of Choquet simplices, in the finite-dimensional case.

Full work available at URL: https://arxiv.org/abs/1309.7424

zbMATH Keywords

Newton polyhedron simplicial group dimension group affine representation approximately divisible good measure order ideal

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Convex sets in topological linear spaces; Choquet theory (46A55) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) (K_0) as an ordered group, traces (19K14) Dynamical systems and the theory of (C^*)-algebras (37A55)

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