Affine buildings, tiling systems and higher rank Cuntz-Krieger algebras

DOI10.1515/crll.1999.057zbMath1064.46504arXiv1302.5593OpenAlexW2963153751MaRDI QIDQ4260203

Tim Steger, A. Guyan Robertson

Publication date: 2 February 2000

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.5593

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) General theory of (C^*)-algebras (46L05) Groups with a (BN)-pair; buildings (20E42)

Related Items (60)

Prime and primitive Kumjian–Pask algebras ⋮ Simplicity of C*-algebras associated to higher-rank graphs ⋮ On the K-theory of boundaryC*-algebras of Ã₂groups ⋮ BRANCHING SYSTEMS FOR HIGHER-RANK GRAPH C*-ALGEBRAS ⋮ Rank-two graphs whose \(C^*\)-algebras are direct limits of circle algebras ⋮ A GENERALISATION OF HIGHER-RANK GRAPHS ⋮ Homotopy of product systems and K-theory of Cuntz-Nica-Pimsner algebras ⋮ Moves on k-graphs preserving Morita equivalence ⋮ THE K-THEORY OF THE -ALGEBRAS OF 2-RANK GRAPHS ASSOCIATED TO COMPLETE BIPARTITE GRAPHS ⋮ Higher dimensional generalizations of the Thompson groups ⋮ Separable representations, KMS states, and wavelets for higher-rank graphs ⋮ \(K\)-theory for real \(k\)-graph \(C^\ast\)-algebras ⋮ Wavelets and spectral triples for fractal representations of Cuntz algebras ⋮ Purely infinite simple Kumjian-Pask algebras ⋮ Monic representations of finite higher-rank graphs ⋮ Irreducible subshifts associated with \(\widetilde A_{2}\) buildings ⋮ Semigroupoid \(C^{*}\)-algebras ⋮ Deformations of Fell bundles and twisted graph algebras ⋮ Higher dimensional generalizations of the Thompson groups via higher rank graphs ⋮ The cycline subalgebra of a Kumjian-Pask algebra ⋮ \(C^{\star}\)-algebras of higher-rank graphs from groups acting on buildings, and explicit computation of their \(K\)-theory ⋮ The interplay between \(k\)-graphs and the Yang-Baxter equation. ⋮ When is the Cuntz-Krieger algebra of a higher-rank graph approximately finite-dimensional? ⋮ The cyclic and simplicial cohomology of the Cuntz semigroup algebra ⋮ Homology for higher-rank graphs and twisted \(C^*\)-algebras ⋮ Boundary 𝐶*-algebras for acylindrical groups ⋮ Cyclic cohomology of Banach algebras of quivers and their inverse semigroups ⋮ \(C^\ast\)-algebras associated with Hilbert \(C^\ast\)-quad modules of finite type ⋮ The primitive ideals of the Cuntz-Krieger algebra of a row-finite higher-rank graph with no sources ⋮ A generalized Cuntz-Krieger uniqueness theorem for higher-rank graphs ⋮ KMS states on \(C^\ast\)-algebras associated to higher-rank graphs ⋮ Spectral triples for higher-rank graph $C^*$-algebras ⋮ A dual graph construction for higher-rank graphs, and 𝐾-theory for finite 2-graphs ⋮ Generalised morphisms of 𝑘-graphs: 𝑘-morphs ⋮ Atomic representations of rank 2 graph algebras ⋮ KMS weights on higher rank buildings ⋮ Cohn path algebras of higher-rank graphs ⋮ Computing the fundamental group of a higher-rank graph ⋮ An étale equivalence relation on a tiling space arising from a two-sided subshift and associatedC*-algebras ⋮ Coverings of \(k\)-graphs ⋮ Slightly larger than a graph \(C^*\)-algebra ⋮ Harmonic cochains and K-theory for \(\tilde{A}_2\)-groups ⋮ Product systems over right-angled Artin semigroups ⋮ Cohomology for small categories: \(k\)-graphs and groupoids ⋮ Boundary \(C^\ast\)-algebras of triangle geometries ⋮ Simplicity of \(C^*\)-algebras associated to row-finite locally convex higher-rank graphs ⋮ Cycline subalgebras of 𝑘-graph C*-algebras ⋮ Primitive ideal space of higher-rank graph \(C^\ast\)-algebras and decomposability ⋮ The universal Boolean inverse semigroup presented by the abstract Cuntz-Krieger relations ⋮ Simplicity of twisted \(C^\ast\)-algebras of higher-rank graphs and crossed products by quasifree actions ⋮ Operator algebras for higher rank analysis and their application to factorial languages ⋮ COVERINGS OF SKEW-PRODUCTS AND CROSSED PRODUCTS BY COACTIONS ⋮ A family of 2-graphs arising from two-dimensional subshifts ⋮ Isomorphism of the cubical and categorical cohomology groups of a higher-rank graph ⋮ Kumjian-Pask algebras of higher-rank graphs ⋮ Simple purely infinite \(C^*\)-algebras and \(n\)-filling actions ⋮ On twisted higher-rank graph 𝐶*-algebras ⋮ \(E\)-theoretic duality for higher rank graph algebras ⋮ A groupoid generalisation of Leavitt path algebras ⋮ \(C^\ast\)-algebras associated with Hilbert \(C^\ast\)-quad modules of \(C^\ast\)-textile dynamical systems

This page was built for publication: Affine buildings, tiling systems and higher rank Cuntz-Krieger algebras