Exel, Ruy; Laca, Marcelo Cuntz-Krieger algebras for infinite matrices. (English) Zbl 0932.47053 J. Reine Angew. Math. 512, 119-172 (1999). Authors’ abstract: Given an arbitrary infinite matrix \(A= \{A(i,j)\}_{i,j\in{\mathcal G}}\) with entries in \(\{0,1\}\) and having no identically zero rows, we define an algebra \({\mathcal O}_A\) 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 \({\mathcal O}_A\) 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. \({\mathcal O}_A\) is always nuclear and we obtain conditions for it to be unital and purely infinite. Reviewer: M.Brešar (Maribor) Cited in 3 ReviewsCited in 74 Documents MSC: 47L65 Crossed product algebras (analytic crossed products) 46L05 General theory of \(C^*\)-algebras Keywords:partial isometries; crossed product algebra; partial dynamical system; uniqueness theorem; nuclear; purely infinite PDFBibTeX XMLCite \textit{R. Exel} and \textit{M. Laca}, J. Reine Angew. Math. 512, 119--172 (1999; Zbl 0932.47053) Full Text: DOI arXiv