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Classification of anomalous actions of finite groups with the Rokhlin property

  • Sergio Girón Pacheco
  • Gábor Szabó
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Abstract

Given a finite group G, we develop a generalization of the fundamental classification of Rokhlin G-actions on C*-algebras to the setting of anomalous G-actions with the Rokhlin property. For Rokhlin G-kernels on C*-algebras covered by the classification program, this implies that the induced G-action on some known invariants determines the conjugacy class. Extending a result of Izumi, we show that G-kernels with the Rokhlin property on Kirchberg algebras are classified by their anomaly and the induced module structure on the K-theory groups. We explore K-theoretic obstructions for the existence of Rokhlin G-kernels on general separable C*-algebras and use these to characterise which G-module structures arise as K-groups of Kirchberg algebras admitting a Rokhlin G-kernel with a given lifting obstruction.

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Cite

BibTeXRIS
BibTeX
@misc{pacheco2026classification,
  title = {{Classification of anomalous actions of finite groups with the Rokhlin property}},
  author = {Sergio Girón Pacheco and Gábor Szabó},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.09517},
  eprint = {2608.09517},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.09517},
}
RIS
TY  - UNPB
TI  - Classification of anomalous actions of finite groups with the Rokhlin property
AU  - Sergio Girón Pacheco
AU  - Gábor Szabó
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.09517
UR  - https://arxiv.org/abs/2608.09517
AB  - Given a finite group G, we develop a generalization of the fundamental classification of Rokhlin G-actions on C*-algebras to the setting of anomalous G-actions with the Rokhlin property. For Rokhlin G-kernels on C*-algebras covered by the classification program, this implies that the induced G-action on some known invariants determines the conjugacy class. Extending a result of Izumi, we show that G-kernels with the Rokhlin property on Kirchberg algebras are classified by their anomaly and the induced module structure on the K-theory groups. We explore K-theoretic obstructions for the existence of Rokhlin G-kernels on general separable C*-algebras and use these to characterise which G-module structures arise as K-groups of Kirchberg algebras admitting a Rokhlin G-kernel with a given lifting obstruction.
ER  -