Faithfulness of highest-weight modules for Iwasawa algebras in type D
Stephen Mann
TL;DR
This paper proves that infinite-dimensional highest-weight modules are faithful for Iwasawa algebras of type D Lie algebras, leading to the conclusion that all non-zero two-sided ideals have finite codimension.
Contribution
It establishes faithfulness of highest-weight modules for type D Iwasawa algebras and characterizes their ideals, a novel result in this area.
Findings
Infinite-dimensional highest-weight modules are faithful for type D Iwasawa algebras.
All non-zero two-sided ideals have finite codimension in these algebras.
Provides new insights into the structure of Iwasawa algebras of type D.
Abstract
We prove that infinite-dimensional highest-weight modules are faithful for Iwasawa algebras corresponding to a simple Lie algebra of type D. We use this to prove that all non-zero two-sided ideals of the Iwasawa algebra have finite codimension in this case.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Rings, Modules, and Algebras · Commutative Algebra and Its Applications