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PreprintCC BY 4.0arXiv

Unital embeddings of the Jiang--Su algebra are not unique

  • Matteo Pagliero
Open at sourcePDFDOICite

Abstract

We show that the canonical embeddings of the Jiang--Su algebra 𝒵 into the universal unital free product 𝒵 ∗ℂ𝒵 are not approximately unitarily equivalent. This answers one of the $99$ problems in the list of Schafhauser, Tikuisis, and White. By contrast, we prove that any two such embeddings into a simple, unital, monotracial C∗-algebra with strict comparison by the unique trace are strongly asymptotically unitarily equivalent.

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Cite

BibTeXRIS
BibTeX
@misc{pagliero2026unital,
  title = {{Unital embeddings of the Jiang--Su algebra are not unique}},
  author = {Matteo Pagliero},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02174},
  eprint = {2610.02174},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02174},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Unital embeddings of the Jiang--Su algebra are not unique
AU  - Matteo Pagliero
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.02174
UR  - https://arxiv.org/abs/2610.02174
AB  - We show that the canonical embeddings of the Jiang--Su algebra 𝒵 into the universal unital free product 𝒵 ∗_ℂ𝒵 are not approximately unitarily equivalent. This answers one of the $99$ problems in the list of Schafhauser, Tikuisis, and White. By contrast, we prove that any two such embeddings into a simple, unital, monotracial C^∗-algebra with strict comparison by the unique trace are strongly asymptotically unitarily equivalent.
ER  -