Groups acting on products of trees, tiling systems and analytic K-theory

Title: Groups acting on products of trees, tiling systems and analytic K-theory
Creator: Kimberley, Jason S.; Robertson, Guyan
Relation: New York Journal of Mathematics Vol. 8, p. 111-131
Relation: http://nyjm.albany.edu:8000/j/2002/8_111.html
Publisher: Electronic Journals Project, University at Albany, Department of Mathematics & Science
Resource Type: journal article
Date: 2002
Description: Let T₁ and T₂ be homogeneous trees of even degree ≥ 4. A BM group Γ is a torsion-free discrete subgroup of Aut(T₁)×Aut(T₂) which acts freely and transitively on the vertex set of T₁×T₂. This article studies dynamical systems associated with BM groups. A higher rank Cuntz-Krieger algebra A(Γ) is associated both with a 2-dimensional tiling system and with a boundary action of a BM group Γ. An explicit expression is given for the K-theory of A(Γ). In particular K₀=K₁. A complete enumeration of possible BM groups Γ is given for a product homogeneous trees of degree 4, and the K-groups are computed.
Subject: group actions; trees; K-theory; C*-algebras
Identifier: http://hdl.handle.net/1959.13/38305
Identifier: uon:4294
Identifier: ISSN:1076-9803
Language: eng
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