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 - 2002 |
Externally published | Yes |
Keywords
- Crossed product
- Cuntz-Krieger algebra
- Faithful representation
- Partial action
- Partial group algebra
- Partial representation
ASJC Scopus subject areas
- Algebra and Number Theory