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Classifiable C*-algebras have quantum symmetries
Abstract
We show that every classifiable simple C*-algebra, in particular the Jiang-Su algebra, admits outer actions of several discrete quantum groups, such as finite quantum groups and duals of certain free compact quantum groups. As a consequence of the construction, we provide new examples of hyperfinite subfactors with the Temperley-Lieb-Jones standard invariant and show that SUq(2) can act minimally on some Araki-Woods factors for infinitely many q.
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BibTeX
@misc{kitamura2026classifiable,
title = {{Classifiable C*-algebras have quantum symmetries}},
author = {Kan Kitamura},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16999},
eprint = {2609.16999},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16999},
}
RIS
TY - UNPB
TI - Classifiable C*-algebras have quantum symmetries
AU - Kan Kitamura
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16999
UR - https://arxiv.org/abs/2609.16999
AB - We show that every classifiable simple C*-algebra, in particular the Jiang-Su algebra, admits outer actions of several discrete quantum groups, such as finite quantum groups and duals of certain free compact quantum groups. As a consequence of the construction, we provide new examples of hyperfinite subfactors with the Temperley-Lieb-Jones standard invariant and show that SU_q(2) can act minimally on some Araki-Woods factors for infinitely many q.
ER -