4 citations · 4 across the 3 of their papers we have counts for
8 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…
On the Basis of the Burnside Ring of a Fusion System
Matthew Gelvin, Sune Precht Reeh, Ergun Yalcin
We consider the Burnside ring of -stable -sets for a saturated fusion system defined on a -group . It is shown by S. P. Reeh th…
Minimal characteristic bisets for fusion systems
Matthew Gelvin, Sune Precht Reeh
We show that every saturated fusion system has a unique minimal -characteristic biset . We examine the relationship of wit…
Homotopy equivalences between p-subgroup categories
Matthew Gelvin, Jesper Møller
Let p be a prime number and G a finite group of order divisible by p. Quillen showed that the Brown poset of nonidentity p-subgroups of G is homotopy equivalent to its subposet of…
Fusion Action Systems
Matthew Gelvin
This paper introduces the notion of fusion action system, an abstraction of the -local data of a finite group acting on a finite set. Fusion action systems are closely connected…