Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zappa-Sz\'ep products of semigroups and their C*-algebras   Zappa-Sz\'ep products of semigroups encompass both the self-similar group
actions of Nekrashevych and the quasi-lattice-ordered groups of Nica. We use
Li's construction of semigroup $C^*$-algebras to associate a $C^*$-algebra to
Zappa-Sz\'ep products and give an explicit presentation of the algebra. We then
define a quotient $C^*$-algebra that generalises the Cuntz-Pimsner algebras for
self-similar actions. We indicate how known examples, previously viewed as
distinct classes, fit into our unifying framework. We specifically discuss the
Baumslag-Solitar groups, the binary adding machine, the semigroup
$\mathbb{N}\rtimes\mathbb{N}^\times$, and the $ax+b$-semigroup
$\mathbb{Z}\rtimes\mathbb{Z}^\times$.

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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci