QDQ vs. UCT
Abstract
This is a survey of recent progress in the structure and classification theory of nuclear C*-algebras. In particular, I outline how the Universal Coefficient Theorem ensures a positive answer to the quasidiagonality question in the presence of faithful traces. This has strong consequences for the regularity conjecture and the classification problem for separable, simple, nuclear C*-algebras. Moreover, it entails a positive solution to Rosenberg's conjecture on quasidiagonality of reduced C*-algebras of discrete amenable groups. This note is largely based on a joint paper with Aaron Tikuisis and Stuart White.
Keywords
Cite
@article{arxiv.1603.01493,
title = {QDQ vs. UCT},
author = {Wilhelm Winter},
journal= {arXiv preprint arXiv:1603.01493},
year = {2016}
}
Comments
21 pages; survey article largely based on arXiv:1509.08318; some small corrections and adjustments in v2; intended for Proceedings of the 2015 Abel Symposium