On the separability of some Green biset functors
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911578009370624 |
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| author | Bouc, Serge Romero, Nadia |
| author_facet | Bouc, Serge Romero, Nadia |
| contents | We show that the Green biset functor $R_{\mathbb{C}}$ of complex characters over $\mathbb{Z}$, is not separable, i.e. it is not projective as a bimodule over itself. Also, we show that $RB_G$, the Burnside biset functor shifted by a finite group $G$, over a commutative ring $R$, is separable if and only if $|G|$ is invertible in $R$. Finally, to address the question of the relation between functors and their evaluations, we show that the Burnside $R$-algebra $RB(G)$ is separable if and only if $|G|$ is invertible in $R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07627 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the separability of some Green biset functors Bouc, Serge Romero, Nadia Group Theory Category Theory Rings and Algebras Representation Theory 16Y99, 18D99, 18M05, 20J15 We show that the Green biset functor $R_{\mathbb{C}}$ of complex characters over $\mathbb{Z}$, is not separable, i.e. it is not projective as a bimodule over itself. Also, we show that $RB_G$, the Burnside biset functor shifted by a finite group $G$, over a commutative ring $R$, is separable if and only if $|G|$ is invertible in $R$. Finally, to address the question of the relation between functors and their evaluations, we show that the Burnside $R$-algebra $RB(G)$ is separable if and only if $|G|$ is invertible in $R$. |
| title | On the separability of some Green biset functors |
| topic | Group Theory Category Theory Rings and Algebras Representation Theory 16Y99, 18D99, 18M05, 20J15 |
| url | https://arxiv.org/abs/2604.07627 |