Illinois Journal of Mathematics

Realizing dimension groups, good measures, and Toeplitz factors

David Handelman

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Motivated by connections between dimension groups and good measures or minimal actions on Cantor sets (especially Töplitz), we find realizations of classes of dimension groups as limits of primitive matrices all of which have equal column sums, or equal row sums.

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Illinois J. Math., Volume 57, Number 4 (2013), 1057-1109.

First available in Project Euclid: 1 December 2014

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Primary: 19K14: $K_0$ as an ordered group, traces 06F20: Ordered abelian groups, Riesz groups, ordered linear spaces [See also 46A40] 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] 15B36: Matrices of integers [See also 11C20] 15B48: Positive matrices and their generalizations; cones of matrices 37A55: Relations with the theory of C-algebras [See mainly 46L55] 20K15: Torsion-free groups, finite rank 20K20: Torsion-free groups, infinite rank


Handelman, David. Realizing dimension groups, good measures, and Toeplitz factors. Illinois J. Math. 57 (2013), no. 4, 1057--1109. doi:10.1215/ijm/1417442563.

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