Uniqueness of the von neumann continuous factor

Pere Ara, Joan Claramunt

Research output: Contribution to journalArticleResearch

3 Citations (Scopus)

Abstract

© Canadian Mathematical Society 2018. For a division ring D, denote by MD the D-ring obtained as the completion of the direct limit lim M2n (D) with respect to the metric induced by its unique rank function. We prove that, for any ultramatricial D-ring B and any non-discrete extremal pseudo-rank function N on B, there is an isomorphism of D-rings B = MD, where B stands for the completion of B with respect to the pseudo-metric induced by N. This generalizes a result of von Neumann. We also show a corresponding uniqueness result for ∗-algebras over fields F with positive definite involution, where the algebra MF is endowed with its natural involution coming from the ∗-transpose involution on each of the factors M2n (F).
Original languageEnglish
Pages (from-to)961-982
JournalCanadian Journal of Mathematics
Volume70
DOIs
Publication statusPublished - 1 Oct 2018

Keywords

  • Completion
  • Factor
  • Rank function
  • Ultramatricial
  • Von Neumann regular ring

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