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SUMMARY:Brauer's Main Theorems - Stacey Law\, University of Cambridge
DTSTART:20160205T150000Z
DTEND:20160205T160000Z
UID:TALK64129@talks.cam.ac.uk
CONTACT:Nicolas Dupré
DESCRIPTION:Brauer's Main Theorems are results in the modular representati
 on theory of finite groups that link the blocks of a finite group G with t
 hose of its p-local subgroups. Over characteristic not dividing the group 
 order\, all finite-dimensional modules are projective and the group algebr
 a is semisimple. This unsurprisingly does not hold for a field k of charac
 teristic p dividing |G|\, and we will introduce certain p-subgroups Q of G
  called vertices as measures of 'how far from projective' modules are\, th
 en extend this into the concept of defect groups D for the blocks of the g
 roup algebra. We will see that kG-module structure can be related to that 
 of N_G(Q) and N_G(D) using the Green correspondence and Brauer's Main Theo
 rems\, through small concrete examples as well as theoretical applications
 . 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
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