2007/03/12 by Bouc, Serge
#Category Theory (math.CT) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.math/0703356
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.