Classification of homomorphisms from C(Ω) to a C^*-algebra

2024/08/29 by An, Qingnan, Elliott, George, Liu, Zhichao
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2408.16657

Abstract

Let Ω be a compact subset of ℂ and let A be a unital simple, separable C^*-algebra with stable rank one, real rank zero and strict comparison. We show that, given a Cu-morphism α:\rm Cu(C(Ω))→ \rm Cu(A) with α(⟨ \mathds1_Ω⟩)≤ ⟨ 1_A⟩, there exists a homomorphism ϕ: C(Ω)→ A such that \rm Cu(ϕ)=α and ϕ is unique up to approximate unitary equivalence. We also give classification results for maps from a large class of C^*-algebras to A in terms of the Cuntz semigroup.

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