Unusual properties of group algebras in characteristic
2
John Murray, National University of Ireland, Maynooth
Friday May 19, 4.30-5.15, Groups in Galway 2006
We examine the group algebra of a finite group G as a module for the
wreath product of G with a cyclic group of order 2. Here the cyclic
group acts via the map that sends each group element to its inverse.
Using this framework, the Brauer construction allows us to parametrize
certain real blocks of G in terms of the action of local subgroups on
sets of involutions. We interpret the Frobenius-Schur indicator of a
principal indecomposable character in terms of the rank of a bilinear
form and present a generalization of a theorem of D. Benson and J.
Carlson on the existence of Scott components in the endomorphism rings
of G-modules.