Partial dynamical systems and c*-algebras generated by partial isometries

Ruy Exel, Marcelo Laca, John Quigg

Research output: Contribution to journalArticlepeer-review

77 Scopus citations

Abstract

A collection of partial isometries whose range and initial projections satisfy a specified set of conditions often gives rise to a partial representation of a group. The corresponding C*-algebra is thus a quotient of the universal C*-algebra for partial representations of the group, from which it inherits a crossed product structure, of an abelian C*-algebra by a partial action of the group. This allows us to characterize faithful representations and simplicity, and to study the ideal structure of these C*-algebras in terms of amenability and topological freeness of the associated partial action. We also consider three specific applications: to partial representations of groups, to Toeplitz algebras of quasi-lattice ordered groups, and to Cuntz-Krieger algebras.

Original languageEnglish (US)
Pages (from-to)169-186
Number of pages18
JournalJournal of Operator Theory
Volume47
Issue number1
StatePublished - Jan 1 2002
Externally publishedYes

Keywords

  • Crossed product
  • Cuntz-Krieger algebra
  • Faithful representation
  • Partial action
  • Partial group algebra
  • Partial representation

ASJC Scopus subject areas

  • Algebra and Number Theory

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