New York Journal of Mathematics
Volume 17 (2011) 1-20


Menassie Ephrem

C*-algebra of the Zn-tree

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Published: February 5, 2011
Keywords: Directed graph, Cuntz-Krieger algebra, Graph C*-algebra
Subject: 46L05, 46L35, 46L55

Let Λ = Zn with lexicographic ordering. Λ is a totally ordered group. Let
X = Λ+ * Λ+.
Then X is a Λ-tree. Analogous to the construction of graph C*-algebras, we form a groupoid whose unit space is the space of ends of the tree. The C*-algebra of the Λ-tree is defined as the C*-algebra of this groupoid. We prove some properties of this C*-algebra.

Author information

Department of Mathematics and Statistics, Coastal Carolina University, Conway, SC 29528-6054