Semigroup C*-algebras of $ax+b$-semigroups

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.

23 pages

Cited by in corpus (3)

• On C*-algebras associated to right LCM semigroups
• K-theory for semigroup C*-algebras and partial crossed products
• Algebraic K-theory, K-regularity, and T-duality of ${\mathcal{O}}_{\infty }$-stable $C^{\ast }$-algebras