On the invariant uniform Roe algebra

Takeshi Katsura, Otgonbayar Uuye

Research output: Contribution to journalArticle

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

Fingerprint

Uniform Algebra
Invariant
Group C*-algebra
Discrete Group
Approximation Property
Slice
Subalgebra
Countable
If and only if

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On the invariant uniform Roe algebra. / Katsura, Takeshi; Uuye, Otgonbayar.

In: Journal of Operator Theory, Vol. 72, No. 2, 2014, p. 549-556.

Research output: Contribution to journalArticle

Katsura, Takeshi ; Uuye, Otgonbayar. / On the invariant uniform Roe algebra. In: Journal of Operator Theory. 2014 ; Vol. 72, No. 2. pp. 549-556.
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