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Minimality for noncommutative dynamical systems

  • Thomas Bray
  • Erik Séguin
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Abstract

We consider an alternative notion of minimality for C*-dynamical systems, which we refer to as strong minimality. This notion coincides with the usual definition of minimality in the commutative setting, but diverges sharply from it in the noncommutative setting in a way which we argue addresses several fundamental defects in the usual definition. We demonstrate that strong minimality is deeply connected with Rørdam's notion of a C*-irreducible inclusion, giving a new perspective on the study of such inclusions. We provide various characterizations of this property, including for reduced crossed products, tensor products, and subhomogeneous C*-algebras.

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Cite

BibTeXRIS
BibTeX
@misc{bray2026minimality,
  title = {{Minimality for noncommutative dynamical systems}},
  author = {Thomas Bray and Erik Séguin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04038},
  eprint = {2609.04038},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04038},
}
RIS
TY  - UNPB
TI  - Minimality for noncommutative dynamical systems
AU  - Thomas Bray
AU  - Erik Séguin
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.04038
UR  - https://arxiv.org/abs/2609.04038
AB  - We consider an alternative notion of minimality for C*-dynamical systems, which we refer to as strong minimality. This notion coincides with the usual definition of minimality in the commutative setting, but diverges sharply from it in the noncommutative setting in a way which we argue addresses several fundamental defects in the usual definition. We demonstrate that strong minimality is deeply connected with Rørdam's notion of a C*-irreducible inclusion, giving a new perspective on the study of such inclusions. We provide various characterizations of this property, including for reduced crossed products, tensor products, and subhomogeneous C*-algebras.
ER  -