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CATEGORIES:Junior Algebra/Logic/Number Theory seminar
SUMMARY:The representation theory of Lie algebras: ordinar
y vs modular - Lewis Topley Norwich University
DTSTART;TZID=Europe/London:20131108T150000
DTEND;TZID=Europe/London:20131108T160000
UID:TALK48790AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/48790
DESCRIPTION:A Lie algebra is a structure we attach to a matrix
group\, which encodes many of its algebraic prope
rties. The representation theory of Lie algebras h
as great applications in physics\, which I shall n
ot discuss.\n\nThe theory of highest weight repres
entations is now one of the most prolific and usef
ul concepts in representation theory. In this talk
\, I shall recall how the representation of Lie al
gebras over fields of characteristic zero (the `or
dinary' case) were first classified using highest
weight modules.\n\nIn the second part of the talk
I shall compare the known results in characteristi
c zero to the more mysterious modular realm\, wher
e our Lie algebra is defined over fields of positi
ve characteristic. Here we see that the simple mod
ules have bounded dimension\, and a full classific
ation of simple modules in not known in general. I
shall try to describe some of the useful concepts
involved in studying the theory\, and compare to
the ordinary case.
LOCATION:CMS\, MR5
CONTACT:Julian Brough
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