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Obstructions to the full Hao-Ng isomorphism

  • Adam Dor-On
  • Ian Thompson
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Abstract

We show that the Hao-Ng isomorphism for full crossed products fails to hold. More precisely, for a non-degenerate C*-correspondence X over a C*-algebra π’œ and a generalized gauge action G curvearrowright X by a locally compact group G, we isolate three structural obstructions for the canonical commutation π’ͺXrtimes G β‰… π’ͺXrtimes G between full crossed product and Cuntz-Pimsner C*-algebra. The first concerns hyperrigidity, the second concerns WEP of the coefficient C*-algebra π’œ for trivial actions, and the third concerns the coincidence of full and reduced crossed products by the action of G on π’œ.

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Cite

BibTeXRIS
BibTeX
@misc{doron2026obstructions,
  title = {{Obstructions to the full Hao-Ng isomorphism}},
  author = {Adam Dor-On and Ian Thompson},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.31050},
  eprint = {2608.31050},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.31050},
}
RIS
TY  - UNPB
TI  - Obstructions to the full Hao-Ng isomorphism
AU  - Adam Dor-On
AU  - Ian Thompson
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2608.31050
UR  - https://arxiv.org/abs/2608.31050
AB  - We show that the Hao-Ng isomorphism for full crossed products fails to hold. More precisely, for a non-degenerate C^*-correspondence X over a C^*-algebra π’œ and a generalized gauge action G curvearrowright X by a locally compact group G, we isolate three structural obstructions for the canonical commutation π’ͺ_Xrtimes G β‰… π’ͺ_Xrtimes G between full crossed product and Cuntz-Pimsner C^*-algebra. The first concerns hyperrigidity, the second concerns WEP of the coefficient C^*-algebra π’œ for trivial actions, and the third concerns the coincidence of full and reduced crossed products by the action of G on π’œ.
ER  -