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CATEGORIES:Junior Algebra and Number Theory seminar
SUMMARY:Brauer's Main Theorems - Stacey Law\, University o
f Cambridge
DTSTART;TZID=Europe/London:20160205T150000
DTEND;TZID=Europe/London:20160205T160000
UID:TALK64129AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/64129
DESCRIPTION:Brauer's Main Theorems are results in the modular
representation theory of finite groups that link t
he blocks of a finite group G with those of its p-
local subgroups. Over characteristic not dividing
the group order\, all finite-dimensional modules a
re projective and the group algebra is semisimple.
This unsurprisingly does not hold for a field k o
f characteristic p dividing |G|\, and we will intr
oduce certain p-subgroups Q of G called vertices a
s measures of 'how far from projective' modules ar
e\, then extend this into the concept of defect gr
oups D for the blocks of the group algebra. We wil
l see that kG-module structure can be related to t
hat of N_G(Q) and N_G(D) using the Green correspon
dence and Brauer's Main Theorems\, through small c
oncrete examples as well as theoretical applicatio
ns. If there's time we'll also outline Brauer-Dade
theory for cyclic blocks\, where the simples and
indecomposable projectives can be described neatly
using graphs known as Brauer trees.
LOCATION:CMS\, MR4
CONTACT:Nicolas DuprÃ©
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