4 papers
Conjectural invariance with respect to the fusion system of an almost-source algebra
Laurence Barker, Matthew Gelvin
We show that, given an almost-source algebra of a -block of a finite group , then the unit group of contains a basis stabilized by the left and right multiplicative a…
Dade Groups for Finite Groups and Dimension Functions
Matthew Gelvin, Ergun Yalcin
Let be a finite group and an algebraically closed field of characteristic . We define the notion of a Dade -module as a generalization of endo-permutation modules…
Variants on a conjecture relating block source algebras to characteristic bisets
Laurence Barker, Matthew Gelvin
Given a block of a finite group, any source algebra has a basis invariant under the multiplicative actions of the defect group. Is such a basis a characteristic biset of the block…
An observation on the module structure of block algebras
Matthew Gelvin
Let B be a p-block of the finite group G. We observe that the p-fusion of G constrains the module structure of B: Any basis of B that is invariant under the left and right multipli…