Graded blocks of group algebras with dihedral defect groups
Tom 122 / 2011
Colloquium Mathematicum 122 (2011), 149-176 MSC: Primary 16W50; Secondary 20C20, 18E30. DOI: 10.4064/cm122-2-1
We investigate gradings on tame blocks of group algebras whose defect groups are dihedral. For this subfamily of tame blocks we classify gradings up to graded Morita equivalence, we transfer gradings via derived equivalences, and we check the existence, positivity and tightness of gradings. We classify gradings by computing the group of outer automorphisms that fix the isomorphism classes of simple modules.