Boundary Actions for Affine Buildings and Higher Rank Cuntz-Krieger Algebras

Abstract

Let Γ be a group of type rotating automorphisms of an affine building B of type à 2. If Γ acts freely on the vertices of B with finitely many orbits, and if Ω is the (maximal) boundary of B then C(Ω) ⋊ Γ is a p.i.s.u.n. C*-algebra. This algebra has a structure theory analogous to that of a simple Cuntz-Krieger algebra and is the motivation for a theory of higher rank Cuntz-Krieger algebras, which has been developed by T. Steger and G. Robertson. The K-theory of these algebras can be computed explicitly in the rank two case. For the rank two examples of the form C(Ω) ⋊ Γ which arise from boundary actions on à 2 buildings, the two K-groups coincide.KeywordsCayley GraphHomotopy ClassBoundary ActionPartial IsometryInitial VertexThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.