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

Menassie Ephrem

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

Operator Algebras 2011-01-31 v1

Authors: Menassie Ephrem

Abstract

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.

Keywords

C*-algebra Z^n-tree groupoid totally ordered group end space graph C*-algebra

Cite

@article{arxiv.1101.5570,
  title  = {$C^*$-algebra of the $\mathds{Z}^n$-tree},
  author = {Menassie Ephrem},
  journal= {arXiv preprint arXiv:1101.5570},
  year   = {2011}
}

Comments

20 pages

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