Robertson, Guyan; Steger, Tim Affine buildings, tiling systems and higher rank Cuntz-Krieger algebras. (English) Zbl 1064.46504 J. Reine Angew. Math. 513, 115-144 (1999). Summary: To an \(r\)-dimensional subshift of finite type satisfying certain special properties we associate a \(C^*\)-algebra \(\mathcal A\). This algebra is a higher-rank version of a Cuntz-Krieger algebra. In particular, it is simple, purely infinite and nuclear. We study an example: If \(\Gamma\) is a group acting freely on the vertices of an \(\tilde A_2\) building, with finitely many orbits, and if \(\Omega\) is the boundary of that building, then \(C(\Omega)\rtimes\Gamma\) is the algebra associated to a certain two-dimensional subshift. Cited in 6 ReviewsCited in 60 Documents MSC: 46L05 General theory of \(C^*\)-algebras 46L55 Noncommutative dynamical systems 20E42 Groups with a \(BN\)-pair; buildings PDFBibTeX XMLCite \textit{G. Robertson} and \textit{T. Steger}, J. Reine Angew. Math. 513, 115--144 (1999; Zbl 1064.46504) Full Text: DOI arXiv