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math.RT2021
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…
math.RT2020
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…
math.RT2019
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…