Around evaluations of biset functors
Representation Theory
2018-07-24 v3 Group Theory
Abstract
For a non-vanishing group, we show that the evaluation functor induces an equivalence between the category of modules over the double Burnside algebra and a certain category of biset functors. Using this equivalence, we deduce that over a field of characteristic zero, the double Burnside algebra of a non-vanishing group is a quasi-hereditary algebra. We also show that the double Burnside algebra over a field is self-injective if and only if it is semisimple.
Cite
@article{arxiv.1511.03314,
title = {Around evaluations of biset functors},
author = {Baptiste Rognerud},
journal= {arXiv preprint arXiv:1511.03314},
year = {2018}
}
Comments
v2: there is now a part on the exact Borel subalgebras. I also gave a proof '\`a la Bouc-Th\'evenaz'of Barker's Theorem on the semi-simplicity of the category of biset functors. v3: accepted for publication in Annales de l'institut Fourier