On exotic group C*-algebras

Zhong Jin Ruan, Matthew Wiersma

Research output: Contribution to journalArticlepeer-review


Let Γ be a discrete group. A C*-algebra A is an exotic C*-algebra (associated to Γ) if there exist proper surjective C*-quotients C*(Γ)→A→Cr*(Γ) which compose to the canonical quotient C*(Γ)→Cr*(Γ). In this paper, we show that a large class of exotic C*-algebras has poor local properties. More precisely, we demonstrate the failure of local reflexivity, exactness, and local lifting property. Additionally, A does not admit an amenable trace and, hence, is not quasidiagonal and does not have the WEP when A is from the class of exotic C*-algebras defined by Brown and Guentner (see [8]). In order to achieve the main results of this paper, we prove a result which implies the factorization property for the class of discrete groups which are algebraic subgroups of locally compact amenable groups.

Original languageEnglish (US)
Pages (from-to)437-453
Number of pages17
JournalJournal of Functional Analysis
Issue number2
StatePublished - Jul 15 2016


  • -algebras
  • Amenability
  • C
  • Factorization property
  • Local properties of groups and group

ASJC Scopus subject areas

  • Analysis


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