Yoshida algebra for groupoids
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917479189577728 |
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| author | Shiizuka, Keitaro |
| author_facet | Shiizuka, Keitaro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09563 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Yoshida algebra for groupoids Shiizuka, Keitaro Category Theory 19A22, 18B40, 20L05 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. |
| title | Yoshida algebra for groupoids |
| topic | Category Theory 19A22, 18B40, 20L05 |
| url | https://arxiv.org/abs/2605.09563 |