Finite dimensional ordered vector spaces with Riesz interpolation and Effros-Shen's unimodularity conjecture
Rings and Algebras
2011-11-01 v1 Functional Analysis
K-Theory and Homology
Operator Algebras
Abstract
It is shown that, for any field F \subseteq R, any ordered vector space structure of F^n with Riesz interpolation is given by an inductive limit of sequence with finite stages (F^n,\F_{>= 0}^n) (where n does not change). This relates to a conjecture of Effros and Shen, since disproven, which is given by the same statement, except with F replaced by the integers, Z. Indeed, it shows that although Effros and Shen's conjecture is false, it is true after tensoring with Q.
Keywords
Cite
@article{arxiv.1110.6851,
title = {Finite dimensional ordered vector spaces with Riesz interpolation and Effros-Shen's unimodularity conjecture},
author = {Aaron Tikuisis},
journal= {arXiv preprint arXiv:1110.6851},
year = {2011}
}
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11 pages