Equal column sum and equal row sum dimension group realizations

Abstract

Motivated by connections between minimal actions, especially Töplitz, on Cantor sets, and dimension groups, 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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• Toeplitz flows and their ordered K-theory
• The ultrasimplicial property for simple dimension groups with unique state, the image of which has rank one
• Perfect orderings on Bratteli diagrams II: general Bratteli diagrams