Logic and $\mathrm{C}^*$-algebras: set theoretical dichotomies in the theory of continuous quotients

Alessandro Vignati

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arXiv · 1706.06393

Logic and $\mathrm{C}^*$-algebras: set theoretical dichotomies in the theory of continuous quotients

Alessandro Vignati

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Abstract

Given a nonunital $\mathrm{C}^*$-algebra $A$ one constructs its corona algebra $\mathcal M(A)/A$. This is the noncommutative analog of the \v{C}ech-Stone remainder of a topological space. We analyze the two faces of these algebras: the first one is given assuming CH, and the other one arises when Forcing Axioms are assumed. In their first face, corona $\mathrm{C}^*$-algebras have a large group of automorphisms that includes nondefinable ones. The second face is the Forcing Axiom one; here the automorphism group of a corona $\mathrm{C}^*$-algebra is as rigid as possible, including only definable elements

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BibTeX RIS

Alessandro Vignati. 2017-06-20. Logic and $\mathrm{C}^*$-algebras: set theoretical dichotomies in the theory of continuous quotients. https://arxiv.org/abs/1706.06393

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