Forcing axioms and trivial automorphisms of corona algebras

Let AA be a separable, non-unital C*-algebra, and let Q(A)Q(A) denote its corona algebra. An automorphism of Q(A)Q(A) is trivial if its graph, viewed in the multiplier algebra with the strict topology, is Borel; a nontrivial automorphism is one that is not trivial.

Forcing-axiom conjecture. Forcing axioms imply that Q(A)Q(A) has only trivial automorphisms.

This conjecture is the forcing-axiom counterpart to the Continuum Hypothesis assertion: it predicts rigidity of corona algebras under suitable additional set-theoretic axioms. The source does not specify whether it has been resolved.

Sources & referencesView supporting material

Primary source

Samuel Coskey and Ilijas Farah, “Automorphisms of corona algebras, and group cohomology”, arXiv:1204.4839 (2014).

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