Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $C^*$-algebra of the $\mathds{Z}^n$-tree   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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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph