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PreprintCC0arXiv

Generalized amenability in quantum groups

  • Fouad Naderi
  • Yong Zhang
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Abstract

We study generalized amenability of locally compact quantum groups 𝔾=(scr M, Δ, ϕ, ψ). Let Cr*(𝔾) and VN(𝔾) denote, respectively, the C*-algebra and von Neumann algebra generated by the quantum left regular representation of 𝔾. With natural covariance assumptions and a traceability condition on VN(𝔾), we show that if Cr*(𝔾) is approximately amenable, then 𝔾 admits an invariant quantum mean. We show further that the same conclusion holds if the predual algebra scr M* has a bounded approximate identity and is approximately amenable.

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Cite

BibTeXRIS
BibTeX
@misc{naderi2026generalized,
  title = {{Generalized amenability in quantum groups}},
  author = {Fouad Naderi and Yong Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17451},
  eprint = {2609.17451},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17451},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Generalized amenability in quantum groups
AU  - Fouad Naderi
AU  - Yong Zhang
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17451
UR  - https://arxiv.org/abs/2609.17451
AB  - We study generalized amenability of locally compact quantum groups 𝔾=(scr M, Δ, ϕ, ψ). Let C_r^*(𝔾) and VN(𝔾) denote, respectively, the C*-algebra and von Neumann algebra generated by the quantum left regular representation of 𝔾. With natural covariance assumptions and a traceability condition on VN(𝔾), we show that if C_r^*(𝔾) is approximately amenable, then 𝔾 admits an invariant quantum mean. We show further that the same conclusion holds if the predual algebra scr M_* has a bounded approximate identity and is approximately amenable.
ER  -