The noncommutative weak Extension Principle

Alessandro Vignati; Deniz Yilmaz

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arXiv · 2511.03607

The noncommutative weak Extension Principle

Alessandro Vignati·Deniz Yilmaz

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Abstract

We introduce and study the noncommutative weak Extension Principle, a lifting principle aiming to characterise $^*$-homomorphisms between coronas of nonunital separable $\mathrm{C}^*$-algebras. While this principle fails if the Continuum Hypothesis is assumed, we show that this principle holds under mild forcing axioms such as the Open Colouring Axiom and Martin's Axiom. Further, we introduce and study the notion of nonmeagre ideals in multipliers and coronas of noncommutative $\mathrm{C}^*$-algebras, generalising the usual notion of nonmeagre ideals in $\mathcal P(\mathbb N)$.

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BibTeX RIS

Alessandro Vignati, Deniz Yilmaz. 2025-11-05. The noncommutative weak Extension Principle. https://arxiv.org/abs/2511.03607

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