### Abstract

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 | |

Publication status | Published - Oct 2016 |

### Fingerprint

### Keywords

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

### Cite this

**Finite dimensional ordered vector spaces with Riesz interpolation and Effros-Shen's unimodularity conjecture.** / Tikuisis, Aaron.

Research output: Contribution to journal › Article

*Journal of the Australian Mathematical Society*, vol. 101, no. 2, pp. 277-287. https://doi.org/10.1017/S1446788716000033

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TY - JOUR

T1 - Finite dimensional ordered vector spaces with Riesz interpolation and Effros-Shen's unimodularity conjecture

AU - Tikuisis, Aaron

PY - 2016/10

Y1 - 2016/10

N2 - 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.

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

KW - ordered vector spaces

KW - unimodularity conjecture

KW - simplicial groups

KW - lattice-ordered groups

U2 - 10.1017/S1446788716000033

DO - 10.1017/S1446788716000033

M3 - Article

VL - 101

SP - 277

EP - 287

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

SN - 1446-7887

IS - 2

ER -