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Yoshida algebra for groupoids

  • Keitaro Shiizuka
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Abstract

In this paper, we extend the notion of the Yoshida algebra of a finite group introduced in \cite{Yos83} to finite groupoids and investigate its fundamental properties. Our main results show that the center of the Yoshida algebra of a finite groupoid is isomorphic to the center of the corresponding groupoid algebra, and that there exists a surjective ring homomorphism from the crossed Burnside ring of a finite groupoid, introduced in \cite{Shi26+}, onto the center of the Yoshida algebra of a finite groupoid.

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Cite

BibTeXRIS
BibTeX
@misc{shiizuka2026yoshida,
  title = {{Yoshida algebra for groupoids}},
  author = {Keitaro Shiizuka},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.09563},
  eprint = {2605.09563},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.09563},
}
RIS
TY  - UNPB
TI  - Yoshida algebra for groupoids
AU  - Keitaro Shiizuka
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2605.09563
UR  - https://arxiv.org/abs/2605.09563
AB  - In this paper, we extend the notion of the Yoshida algebra of a finite group introduced in \cite{Yos83} to finite groupoids and investigate its fundamental properties. Our main results show that the center of the Yoshida algebra of a finite groupoid is isomorphic to the center of the corresponding groupoid algebra, and that there exists a surjective ring homomorphism from the crossed Burnside ring of a finite groupoid, introduced in \cite{Shi26+}, onto the center of the Yoshida algebra of a finite groupoid.
ER  -