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Peer-reviewedCC BY 4.0Journal of the London Mathematical Society

Generalized free wreath products and their operator algebras

  • Pierre Fima
  • Arthur Troupel
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Abstract

We develop a new approach on free wreath products, generalizing the constructions of Bichon and of Fima‐Pittau. We show stability properties for certain approximation properties such as exactness, Haagerup property, hyperlinearity, and K‐amenability. We study qualitative properties of the associated von Neumann algebra: factoriality, primeness, and absence of Cartan subalgebra and we give a formula for Connes' T‐invariant. Finally, we give some explicit computations of K‐theory groups for C*‐algebras of generalized free wreath products.

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Cite

BibTeXRIS
BibTeX
@article{fima2026generalized,
  title = {{Generalized free wreath products and their operator algebras}},
  author = {Pierre Fima and Arthur Troupel},
  journal = {Journal of the London Mathematical Society},
  year = {2026},
  month = jun,
  doi = {10.1112/jlms.70595},
  eprint = {2504.00596},
  archivePrefix = {arXiv},
  url = {https://universite-paris-saclay.hal.science/hal-05739103v1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Generalized free wreath products and their operator algebras
AU  - Pierre Fima
AU  - Arthur Troupel
PY  - 2026
DA  - 2026/06/22
JO  - Journal of the London Mathematical Society
DO  - 10.1112/jlms.70595
UR  - https://universite-paris-saclay.hal.science/hal-05739103v1
AB  - We develop a new approach on free wreath products, generalizing the constructions of Bichon and of Fima‐Pittau. We show stability properties for certain approximation properties such as exactness, Haagerup property, hyperlinearity, and K‐amenability. We study qualitative properties of the associated von Neumann algebra: factoriality, primeness, and absence of Cartan subalgebra and we give a formula for Connes' T‐invariant. Finally, we give some explicit computations of K‐theory groups for C*‐algebras of generalized free wreath products.
SN  - 0024-6107
SN  - 1469-7750
ER  -