The noncommutative weak extension principle

Alessandro Vignati and Deniz Yilmaz

Vol. 345 (2026), No. 1, 187–224

DOI: 10.2140/pjm.2026.345.187

Abstract

We introduce and study the noncommutative weak extension principle, a lifting principle that characterises $\ast$-homomorphisms between coronas of nonunital separable ${C<!--FUNCTION\; APPLICATION-->}^{\ast }$-algebras. While this principle fails if the continuum hypothesis is assumed, we show its validity under mild forcing axioms, namely, the open colouring axiom and Martin’s axiom. Also, we introduce and study the notion of nonmeagre ideals in multipliers and coronas of noncommutative ${C<!--FUNCTION\; APPLICATION-->}^{\ast }$-algebras, generalising the usual notion of nonmeagre ideals in $\mathcal{𝒫}(\mathbb{N})$.

Keywords

corona C*-algebras, weak extension principle, forcing axioms

Mathematical Subject Classification

Primary: 03E35, 46L05

Secondary: 46L85

Milestones

Received: 10 November 2025

Revised: 18 June 2026

Accepted: 14 July 2026

Published: 25 September 2026