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PreprintCC BY-NC-SA 4.0arXiv

Non-MF groups and non-finite full group C*-algebras

  • Caleb Eckhardt
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Abstract

Let Γ be a property (T) group admitting an injective, non-surjective endomorphism and let G be the associated ascending HNN-extension. Let W=(⨁G/Γ ℤ/2ℤ) rtimes G. We show that W is not an MF group and that C*(G) is not a finite C*-algebra. The ideas and proofs were generated by ChatGPT 5.6 Sol, we have only refined their arguments in a hopefully more palatable form.

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Cite

BibTeXRIS
BibTeX
@misc{eckhardt2026nonmf,
  title = {{Non-MF groups and non-finite full group C*-algebras}},
  author = {Caleb Eckhardt},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.28772},
  eprint = {2608.28772},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28772},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Non-MF groups and non-finite full group C*-algebras
AU  - Caleb Eckhardt
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.28772
UR  - https://arxiv.org/abs/2608.28772
AB  - Let Γ be a property (T) group admitting an injective, non-surjective endomorphism and let G be the associated ascending HNN-extension. Let W=(⨁_G/Γ ℤ/2ℤ) rtimes G. We show that W is not an MF group and that C^*(G) is not a finite C*-algebra. The ideas and proofs were generated by ChatGPT 5.6 Sol, we have only refined their arguments in a hopefully more palatable form.
ER  -