Semigroup 𝐶*-algebras of 𝑎𝑥+𝑏-semigroups

Li, Xin

doi:10.1090/tran/6469

Semigroup $C^*$-algebras of $ax+b$-semigroups
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Trans. Amer. Math. Soc. 368 (2016), 4417-4437 Request permission

Abstract:

We study semigroup $C^*$-algebras of $ax+b$-semigroups over integral domains. The goal is to generalize several results about $C^*$-algebras of $ax+b$-semigroups over rings of algebraic integers. We prove results concerning K-theory and structural properties like the ideal structure or pure infiniteness. Our methods allow us to treat $ax+b$-semigroups over a large class of integral domains containing all noetherian, integrally closed domains and coordinate rings of affine varieties over infinite fields.

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Semigroup $C^*$-algebras of $ax+b$-semigroups
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Abstract: