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

Abstract

Let $\Lambda ={\mathbb{Z}}^n$ with lexicographic ordering. $\Lambda$ is a totally ordered group. Let $X={\Lambda }^{+}\ast {\Lambda }^{+}$. Then $X$ is a $\Lambda$-tree. Analogous to the construction of graph $C^{\ast }$-algebras, we form a groupoid whose unit space is the space of ends of the tree. The $C^{\ast }$-algebra of the $\Lambda$-tree is defined as the $C^{\ast }$-algebra of this groupoid. We prove some properties of this $C^{\ast }$-algebra.

20 pages

References in corpus (1)

• Characterizing Liminal And Type I Graph C*-Algebras