Rational $p$-biset functors
| dc.creator | Bouc, Serge | |
| dc.date | 2007-03-12 | |
| dc.date.accessioned | 2026-07-07T07:51:41Z | |
| dc.date.available | 2026-07-07T07:51:41Z | |
| dc.description | In this paper, I give several characterizations of {\em rational biset functors over $p$-groups}, which are independent of the knowledge of genetic bases for $p$-groups. I also introduce a construction of new biset functors from known ones, which is similar to the Yoneda construction for representable functors, and to the Dress construction for Mackey functors, and I show that this construction preserves the class of rational $p$-biset functors.\par This leads to a characterization of rational $p$-biset functors as additive functors from a specific quotient category of the biset category to abelian groups. Finally, I give a description of the largest rational quotient of the Burnside $p$-biset functor : when $p$ is odd, this is simply the functor $R_\Q$ of rational representations, but when $p=2$, it is a non split extension of $R_\Q$ by a specific uniserial functor, which happens to be closely related to the functor of units of the Burnside ring. | |
| dc.identifier | https://arxiv.org/abs/math/0703356 | |
| dc.identifier | http://arxiv.org/abs/math/0703356 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125604 | |
| dc.subject | Group Theory | |
| dc.subject | Category Theory | |
| dc.title | Rational $p$-biset functors | |
| dc.type | text |