Quasi-hereditary property of double Burnside algebras
Representation Theory
2015-11-11 v1 Group Theory
Abstract
In this short note we investigate some consequences of the vanishing of simple biset functors. As corollary, if there is no non-trivial vanishing of simple biset functors (e.g. if the group is commutative), then we show that the double Burnside algebra is a quasi-hereditary algebra in characteristic zero. In general, this not true without the non-vanishing condition, as over a field of characteristic zero, the double Burnside algebra of the alternating group of degree 5 has infinite global dimension.
Keywords
Cite
@article{arxiv.1511.03210,
title = {Quasi-hereditary property of double Burnside algebras},
author = {Baptiste Rognerud},
journal= {arXiv preprint arXiv:1511.03210},
year = {2015}
}
Comments
Accepted for publication in Comptes Rendus Mathematique