The noncommutative weak Extension Principle
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909887985876992 |
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| author | Vignati, Alessandro Yilmaz, Deniz |
| author_facet | Vignati, Alessandro Yilmaz, Deniz |
| contents | 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 $\mathcal P(\mathbb N)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03607 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The noncommutative weak Extension Principle Vignati, Alessandro Yilmaz, Deniz Logic Operator Algebras 03E35, 03E57, 46L05, 46L85 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 $\mathcal P(\mathbb N)$. |
| title | The noncommutative weak Extension Principle |
| topic | Logic Operator Algebras 03E35, 03E57, 46L05, 46L85 |
| url | https://arxiv.org/abs/2511.03607 |