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PreprintCC BY 4.0arXiv

Outer action of representation category of discrete quantum groups: a case study

  • Debashish Goswami
  • Suchetana Samadder
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Abstract

Given any tracial von Neumann algebra π’œ, the first author has defined a unitary tensor functor Ξ¦:Rep(𝒬aut(π’œ))β†’ Bimod(π’œ) in his paper [Gos24]. In this paper, we consider π’œ to be the underlying von Neumann algebra of C*(S3) and show that given any DQG 𝒬, which contains C*(S3) as a quantum subgroup and has an outer action Ξ¦Μƒ (in the sense of Definition 3.4}) on Bimod(π’œ), which agrees with Ξ¦ when restricted on Rep(C*(S3)), is monoidally equivalent to the DQG C*(S3). Furthermore, given any DQG 𝒬 with an outer action Ξ“:Rep(𝒬)β†’ Bimod(π’œ), such that $ {\rm Out}(\mathcal{A})\subseteq {\rm Im}(Ξ“)$, is either monoidally equivalent to Out(π’œ) or monoidally equivalent to C*(S3) itself.

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Cite

BibTeXRIS
BibTeX
@misc{goswami2026outer,
  title = {{Outer action of representation category of discrete quantum groups: a case study}},
  author = {Debashish Goswami and Suchetana Samadder},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39254},
  eprint = {2609.39254},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39254},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Outer action of representation category of discrete quantum groups: a case study
AU  - Debashish Goswami
AU  - Suchetana Samadder
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39254
UR  - https://arxiv.org/abs/2609.39254
AB  - Given any tracial von Neumann algebra π’œ, the first author has defined a unitary tensor functor Ξ¦:Rep(𝒬_aut(π’œ))β†’ Bimod(π’œ) in his paper [Gos24]. In this paper, we consider π’œ to be the underlying von Neumann algebra of C^*(S_3) and show that given any DQG 𝒬, which contains C^*(S_3) as a quantum subgroup and has an outer action Ξ¦Μƒ (in the sense of Definition 3.4}) on Bimod(π’œ), which agrees with Ξ¦ when restricted on Rep(C^*(S_3)), is monoidally equivalent to the DQG C^*(S_3). Furthermore, given any DQG 𝒬 with an outer action Ξ“:Rep(𝒬)β†’ Bimod(π’œ), such that $ {\rm Out}(\mathcal{A})\subseteq {\rm Im}(Ξ“)$, is either monoidally equivalent to Out(π’œ) or monoidally equivalent to C^*(S_3) itself.
ER  -