Finite dimensional ordered vector spaces with Riesz interpolation and Effros-Shen's unimodularity conjecture

Aaron Tikuisis

doi:10.1017/S1446788716000033

Finite dimensional ordered vector spaces with Riesz interpolation and Effros-Shen's unimodularity conjecture

Aaron Tikuisis

Mathematical Science

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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Abstract

It is shown that, for any field F⊆R, any ordered vector space structure of Fn with Riesz interpolation is given by an inductive limit of a sequence with finite stages (Fn,Fn≥0) (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.

Original language	English
Pages (from-to)	277-287
Number of pages	11
Journal	Journal of the Australian Mathematical Society
Volume	101
Issue number	2
Early online date	13 May 2016
DOIs	https://doi.org/10.1017/S1446788716000033
Publication status	Published - Oct 2016

Keywords

dimension groups
Riesz interpolation
ordered vector spaces
unimodularity conjecture
simplicial groups
lattice-ordered groups

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Accepted Manuscript
This article has been published in a revised form inJournal of the Australian Mathematical Society https://doi.org/10.1017/S1446788716000033. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © 2016 Australian Mathematical Publishing Association Inc.
Accepted author manuscript, 330 KBLicence: Unspecified

Cite this

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AB - It is shown that, for any field F⊆R, any ordered vector space structure of Fn with Riesz interpolation is given by an inductive limit of a sequence with finite stages (Fn,Fn≥0) (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.

KW - dimension groups

KW - Riesz interpolation

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KW - simplicial groups

KW - lattice-ordered groups

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JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

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ER -

Finite dimensional ordered vector spaces with Riesz interpolation and Effros-Shen's unimodularity conjecture

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