Faithfulness of highest-weight modules for Iwasawa algebras

We prove faithfulness of infinite-dimensional generalised Verma modules for Iwasawa algebras corresponding to split simple Lie algebras with a Chevalley basis. We use this to prove faithfulness of all infinite-dimensional highest-weight modules in the case of type *A*. In this case we also show that all non-zero two-sided ideals of the corresponding Iwasawa algebras have finite codimension, and in particular all non-zero prime ideals are annihilators of finite-dimensional simple modules.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2022

Author dc:creator

• Mann, Stephen

Advisor dc:contributor.advisor

• Wadsley, Simon James

• Noncommutative Algebra
• Representation Theory

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/2b1f1192-2d0b-4be2-9da1-27575202794b/download
• https://creativecommons.org/licenses/by/4.0/

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.99798

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/353740