PARTIAL DYNAMICAL SYSTEMS AND C -ALGEBRAS GENERATED BY PARTIAL ISOMETRIES

A collection of partial isometries whose range and initial pro- jections satisfy a specified set of conditions often gives rise to a partial rep- resentation 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.