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SUMMARY:Faithfulness of highest-weight modules for Iwasawa algebras - Step
 hen Mann
DTSTART:20220525T153000Z
DTEND:20220525T163000Z
UID:TALK175070@talks.cam.ac.uk
CONTACT:Christopher Brookes
DESCRIPTION:Re: Algebra seminar\nYou replied on Tue 24/05/2022 15:38\nYou 
 replied on Tue 24/05/2022 15:38\nStephen Mann\nTitle: Faithfulness of high
 est-weight modules for Iwasawa algebras\nAbstract: Iwasawa algebras are co
 mpleted group algebras for profinite groups and have applications in Numbe
 r Theory. It is an ongoing project to study the prime ideals of noncommuta
 tive Iwasawa algebras.\n\nIn the case of an Iwasawa algebra KG correspondi
 ng to a split simple Lie algebra\, we can embed KG as a subalgebra of a co
 mpleted enveloping algebra. This allows us to study KG-modules that arise 
 as completions of highest-weight modules.\n\nIf we can show that all infin
 ite-dimensional highest-weight modules are faithful over KG\, it will be p
 ossible to show that all non-zero prime ideals of KG arise as annihilators
  of finite-dimensional simple modules. In this talk I will outline the pro
 gress that has been made towards showing the faithfulness of infinite-dime
 nsional highest-weight modules for KG\, and how this applies to prime idea
 ls of KG.
LOCATION:MR14
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