9 papers
Pointed fusion systems of blocks
Laurence Barker
The pointed fusion system of a block is a structure consisting of the fusions and relative multiplicities between the local pointed groups associated with a maximal Brauer pair. We…
The pointed -groups on a block algebra
Laurence Barker
A pointed -group is a pointed group such that is a -group. We parameterize the pointed -groups on a group algebra or on a block algebra of a group algebra. The p…
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…
Semisimplicity of some deformations of the subgroup category and the biset category
Laurence Barker, İsmail Alperen Öğüt
We introduce some deformations of the biset category and prove a semisimplicity property. We also consider another group category, called the subgroup category, whose morphisms are…
Some deformations of the fibred biset category
Laurence Barker, İsmail Alperen Öğüt
We prove the well-definedness of some deformations of the fibred biset category in characteristic zero. The method is to realize the fibred biset category and the deformations as t…
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…