### 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 language | English (US) |
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Pages (from-to) | 169-186 |

Number of pages | 18 |

Journal | Journal of Operator Theory |

Volume | 47 |

Issue number | 1 |

State | Published - Jan 1 2002 |

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### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Operator Theory*,

*47*(1), 169-186.