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PreprintCC BY-NC-SA 4.0arXiv

Actions of Fell bundles, II: tensor products and Fourier-Stieltjes algebras

  • Erik Bédos
  • Roberto Conti
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Abstract

In the context of Fell bundles over discrete groups, we introduce and analyze suitable notions of direct sum and tensor product of actions of Fell bundles on Hilbert bundles. For C*-dynamical systems, where actions arise from equivariant representations, we discuss how the tensor product of two such actions is related to the action associated with the tensor product of the underlying equivariant representations. Likewise, since any action gives rise to a C*-correspondence between the full cross-sectional C*-algebras of the involved Fell bundles, we examine the connection between the C*-correspondence associated with the tensor product of two given actions and the tensor product of the associated C*-correspondences. We also discuss how the tensor product of actions naturally appears in Rieffel-like induction processes. Finally we present related results on the Fourier-Stieltjes and Fourier algebras of a Fell bundle.

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Cite

BibTeXRIS
BibTeX
@misc{bedos2026actions,
  title = {{Actions of Fell bundles, II: tensor products and Fourier-Stieltjes algebras}},
  author = {Erik Bédos and Roberto Conti},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13646},
  eprint = {2610.13646},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13646},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Actions of Fell bundles, II: tensor products and Fourier-Stieltjes algebras
AU  - Erik Bédos
AU  - Roberto Conti
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13646
UR  - https://arxiv.org/abs/2610.13646
AB  - In the context of Fell bundles over discrete groups, we introduce and analyze suitable notions of direct sum and tensor product of actions of Fell bundles on Hilbert bundles. For C^*-dynamical systems, where actions arise from equivariant representations, we discuss how the tensor product of two such actions is related to the action associated with the tensor product of the underlying equivariant representations. Likewise, since any action gives rise to a C^*-correspondence between the full cross-sectional C^*-algebras of the involved Fell bundles, we examine the connection between the C^*-correspondence associated with the tensor product of two given actions and the tensor product of the associated C^*-correspondences. We also discuss how the tensor product of actions naturally appears in Rieffel-like induction processes. Finally we present related results on the Fourier-Stieltjes and Fourier algebras of a Fell bundle.
ER  -