Zappa-Sz\'ep products of semigroups and their C*-algebras
By Nathan Brownlowe, Jacqui Ramagge, D. Robertson, Michael F. Whittaker. 2013
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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 $\mathbb{Z}\rtimes\mathbb{Z}^\times$.
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e8e9e728fb9018277fd1601aaa1769a75dcb42f5
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In Computational Theory and Mathematics
In Mathematical Physics
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- Boundary quotients of C*-algebras of right LCM semigroups (2014, background): “ght(S)), is identified as a suitable boundary quotient. Our only contribution to the literature for this situation would seem to be the isomorphism between this boundary quotient and the one defined in [BRRW14]. We do note that our result Proposition 4.7 is analogous to [Li13, Proposition 7.20], and i”