## Quasi-hereditary property of double Burnside algebras

In this short note, we investigate some consequences of the vanishing of simple biset functors. As a corollary, if there is no non-trivial vanishing of simple biset functors (e.g., if the group G is commutative), then we show that kB(G,G) is a quasi-hereditary algebra in characteristic zero. In general, this is 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.

Published in:
Comptes Rendus Mathematique, 353, 8, 689-693
Year:
2015
Publisher:
Paris, Elsevier
ISSN:
1631-073X
Laboratories: