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

Aaron Tikuisis

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)277-287
Number of pages11
JournalJournal of the Australian Mathematical Society
Volume101
Issue number2
Early online date13 May 2016
DOIs
Publication statusPublished - Oct 2016

Fingerprint

Ordered Vector Space
Interpolate
Inductive Limit
Integer
False

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.

In: Journal of the Australian Mathematical Society, Vol. 101, No. 2, 10.2016, p. 277-287.

Research output: Contribution to journalArticle

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