On generators of C_r^*(𝔽_2) — Draconitic Research

Abstract

It is shown that the reduced group C*-algebra C_r^*(𝔽₂) is singly generated, where 𝔽₂ is the free group on two generators. With respect to the generator constructed in the paper, the topological free entropy dimension of C_r^*(𝔽₂) is shown to be $2$.

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BibTeX RIS

BibTeX

@misc{elliott2026generators,
  title = {{On generators of $\mathrmC_r^*(\mathbbF_2)$}},
  author = {George A. Elliott and Chun Guang Li and Zhuang Niu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32058},
  eprint = {2609.32058},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32058},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - On generators of C_r^*(𝔽_2)
AU  - George A. Elliott
AU  - Chun Guang Li
AU  - Zhuang Niu
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.32058
UR  - https://arxiv.org/abs/2609.32058
AB  - It is shown that the reduced group C*-algebra C_r^*(𝔽_2) is singly generated, where 𝔽_2 is the free group on two generators. With respect to the generator constructed in the paper, the topological free entropy dimension of C_r^*(𝔽_2) is shown to be $2$.
ER  -