$C^*$-algebra of the $\mathds{Z}^n$-tree

Details $C^*$-algebra of the $\mathds{Z}^n$-tree $C^*$-algebra of the $\mathds{Z}^n$-tree

2011-01-28

arxiv.org/abs/1101.5570v1

Ephrem, M. $C^*$-algebra of the $\mathds{Z}^n$-tree New York J. Math. {\bf 17} (2011), 1--20

Mathematics

Operator Algebras

20 pages

Scientific paper

Let $\Lambda = \mathbb{Z}^n$ with lexicographic ordering. $\Lambda$ is a totally ordered group. Let $X = \Lambda^+ * \Lambda^+$. Then $X$ is a $\Lambda$-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 $\Lambda$-tree is defined as the $C^*$-algebra of this groupoid. We prove some properties of this $C^*$-algebra.

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