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CATEGORIES:Algebra and Representation Theory Seminar
SUMMARY:The Ext algebra of a Brauer graph algebra - Nicole
Snashall\, Leicester
DTSTART;TZID=Europe/London:20131204T163000
DTEND;TZID=Europe/London:20131204T173000
UID:TALK48655AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/48655
DESCRIPTION:Brauer graph algebras are generalizations of Braue
r tree algebras\, which\nwere used\, for group alg
ebras KG over a finite group G\, to study blocks\n
with cyclic defect groups. Brauer graph algebras h
ave since played a major\nrole in the classificati
on of finite-dimensional self-injective algebras\n
of tame representation type.\n\nOne of the fundame
ntal questions is when is the Ext algebra of a giv
en\nalgebra itself finitely generated? This talk w
ill describe the Ext algebra\nof a Brauer graph al
gebra\, as well as discussing various generalizati
ons\nof the Koszul property for Brauer graph algeb
ras. We note that it is\nwell-known that the Ext a
lgebra of a Koszul algebra is generated in\ndegree
s 0 and 1\, so is finitely generated. This is join
t work with Green\,\nSchroll and Taillefer.\n\nIn
order to describe the Ext algebra\, we use a theor
y of coverings of\nBrauer graphs which are compati
ble with coverings of Brauer graph\nalgebras\; thi
s is joint work with Green and Schroll. In particu
lar\, we\nclassify the coverings of Brauer graph a
lgebras that are again Brauer\ngraph algebras\, an
d show that there is a tower of coverings so that
any\nBrauer graph can be covered by a Brauer graph
that has multiplicity\nfunction precisely 1\, no
loops and no multiple edges.
LOCATION:MR12
CONTACT:David Stewart
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