Completeness of the isomorphism problem for separable C*-algebras
Operator Algebras
2013-07-16 v2 Logic
Abstract
We prove that the isomorphism problem for separable nuclear C*-algebras is complete in the class of orbit equivalence relations. In fact, already the isomorphism of simple, separable AI C*-algebras is a complete orbit equivalence relation. This means that any isomorphism problem arsing from a continuous action of a separable completely metrizable group can be reduced to the isomorphism of simple, separable AI C*-algebras. As a consequence, we get that the isomorphism problems for separable nuclear C*-algebras and for separable C*-algebras have the same complexity. This answers questions posed by Elliott, Farah, Paulsen, Rosendal, Toms and T\"ornquist.
Keywords
Cite
@article{arxiv.1306.1049,
title = {Completeness of the isomorphism problem for separable C*-algebras},
author = {Marcin Sabok},
journal= {arXiv preprint arXiv:1306.1049},
year = {2013}
}