Cuntz-Krieger algebras for infinite matrices

Details Cuntz-Krieger algebras for infinite matrices Cuntz-Krieger algebras for infinite matrices

1997-12-18

arxiv.org/abs/funct-an/9712008v2

Mathematics

Operator Algebras

Plain TeX, 40 pages, no figures, A minor error in Theorem 9.1 was corrected

Scientific paper

Given an arbitrary infinite 0--1 matrix A having no identically zero rows, we define an algebra OA as the universal C*-algebra generated by partial isometries subject to conditions that generalize, to the infinite case, those introduced by Cuntz and Krieger for finite matrices. We realize OA as the crossed product algebra for a partial dynamical system and, based on this description, we extend to the infinite case some of the main results known to hold in the finite case, namely the uniqueness theorem, the classification of ideals, and the simplicity criteria. OA is always nuclear and we obtain conditions for it to be unital and purely infinite.

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