University of Sydney
School of Mathematics and Statistics
University of Leicester
The Stable Category of a Finite Group is Locally Determined.
Friday 9th April, 12-1pm, Carslaw 375.
One of the main problems in modular representation theory is to
understand the connections between local and global representations
of a finite group G. In other words, one frequently tries
to understand the representations of G over a field
k of characteristic p>0 by studying
representations for the normalizers of nontrivial
p-subgroups, known as local subgroups. The stable
category kG-Mod is defined by factoring out the
projectives in the category kG-Mod of all left
kG-modules. This talk will discuss a way of using the
local structure of G to construct a category
L(G,k) that is equivalent to kG-Mod. It is
then easy to identify an appropriate subcategory of L(G,k)
that is equivalent to the subcategory kG-mod of
finitely generated modules in kG-Mod.