The Fourier Algebra of Certain Compact Orbit Hypergroups

Abstract

Let R be a compact discrete valuation ring and G = R^d rtimes GL_d(R). We show that the central Fourier algebra ZA(G) is not amenable, reaffirming a conjecture of Alaghmandan and Spronk. Our methods reduce to studying the Fourier algebra of the commutative orbit hypergroup H = R^d/GL_d(R). Along the way, we also show that dual of any commutative orbit hypergroup H is the hypergroup of the corresponding dual action, and this in turn shows that A(H) ≅ L¹(Ĥ), which aligns with the classical setting.

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BibTeX RIS

BibTeX

@misc{vujicic2026fourier,
  title = {{The Fourier Algebra of Certain Compact Orbit Hypergroups}},
  author = {Aleksa Vujičić},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35740},
  eprint = {2609.35740},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35740},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - The Fourier Algebra of Certain Compact Orbit Hypergroups
AU  - Aleksa Vujičić
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.35740
UR  - https://arxiv.org/abs/2609.35740
AB  - Let R be a compact discrete valuation ring and G = R^d rtimes GL_d(R). We show that the central Fourier algebra ZA(G) is not amenable, reaffirming a conjecture of Alaghmandan and Spronk. Our methods reduce to studying the Fourier algebra of the commutative orbit hypergroup H = R^d/GL_d(R). Along the way, we also show that dual of any commutative orbit hypergroup H is the hypergroup of the corresponding dual action, and this in turn shows that A(H) ≅ L^1(Ĥ), which aligns with the classical setting.
ER  -

Abstract

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