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CATEGORIES:Algebra and Representation Theory Seminar
SUMMARY:Faithfulness of highest-weight modules for Iwasawa
algebras - Stephen Mann
DTSTART;TZID=Europe/London:20220525T163000
DTEND;TZID=Europe/London:20220525T173000
UID:TALK175070AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/175070
DESCRIPTION:Re: Algebra seminar\nYou replied on Tue 24/05/2022
15:38\nYou replied on Tue 24/05/2022 15:38\nSteph
en Mann\nTitle: Faithfulness of highest-weight mod
ules for Iwasawa algebras\nAbstract: Iwasawa algeb
ras are completed group algebras for profinite gro
ups and have applications in Number Theory. It is
an ongoing project to study the prime ideals of no
ncommutative Iwasawa algebras.\n\nIn the case of a
n Iwasawa algebra KG corresponding to a split simp
le Lie algebra\, we can embed KG as a subalgebra o
f a completed enveloping algebra. This allows us t
o study KG-modules that arise as completions of hi
ghest-weight modules.\n\nIf we can show that all i
nfinite-dimensional highest-weight modules are fai
thful over KG\, it will be possible to show that a
ll non-zero prime ideals of KG arise as annihilato
rs of finite-dimensional simple modules. In this t
alk I will outline the progress that has been made
towards showing the faithfulness of infinite-dime
nsional highest-weight modules for KG\, and how th
is applies to prime ideals of KG.
LOCATION:MR14
CONTACT:Christopher Brookes
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