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Every classifiable simple C*-algebra has a C*-diagonal
Abstract
We construct C*-diagonals in all UCT Kirchberg algebras. Together with known constructions of C*-diagonals in the stably finite setting by Xin Li, this shows that every classifiable C*-algebra (in the sense of the Elliott classification programme) has a C*-diagonal. In fact, we show that every UCT Kirchberg algebra admits an untwisted principal étale groupoid model with a finite-dimensional unit space.
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BibTeX
@misc{evington2026every,
title = {{Every classifiable simple C*-algebra has a C*-diagonal}},
author = {Samuel Evington and Philipp Sibbel},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04648},
eprint = {2611.04648},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04648},
}
RIS
TY - UNPB
TI - Every classifiable simple C*-algebra has a C*-diagonal
AU - Samuel Evington
AU - Philipp Sibbel
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04648
UR - https://arxiv.org/abs/2611.04648
AB - We construct C*-diagonals in all UCT Kirchberg algebras. Together with known constructions of C*-diagonals in the stably finite setting by Xin Li, this shows that every classifiable C*-algebra (in the sense of the Elliott classification programme) has a C*-diagonal. In fact, we show that every UCT Kirchberg algebra admits an untwisted principal étale groupoid model with a finite-dimensional unit space.
ER -