On the invariant uniform Roe algebra

Takeshi Katsura, Otgonbayar Uuye

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Abstract

Let Γ be a countable discrete group. The invariant uniform Roe algebra of G is the C*-subalgebra of its uniform Roe algebra consisting of Γ-invariant elements. We show that Γ has the approximation property if and only if Γ is exact and the invariant uniform Roe algebra has a certain slice map property. This answers a question of J. Zacharias. We also show that characterisations of several properties of Γ in terms of its reduced group C*-algebra also apply to its invariant uniform Roe algebra.

Original languageEnglish
Pages (from-to)549-556
Number of pages8
JournalJournal of Operator Theory
Volume72
Issue number2
DOIs
Publication statusPublished - 2014 Jan 1

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Keywords

  • Approximation property
  • Invariant translation approximation property
  • Operator approximation property
  • Uniform Roe algebra

ASJC Scopus subject areas

  • Algebra and Number Theory

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