Functor morphing and representations of automorphism groups of modules

2023/08/07 by Tyrone Crisp, Crisp, Tyrone, Ehud Meir +3
Chemistry · Mathematics · #18M05 (Secondary) #20C07 #20C15 #20C33 #22E50 (Primary) 20G25 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Carbohydrate Chemistry and Synthesis #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2308.03248

openalex publication_date 2023/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a strategy to study irreducible representations of automorphism groups of finite modules over local rings. We prove that these automorphism groups fit in a hierarchy that facilitates a stratification of their irreducible representations in terms of smaller building blocks using symmetric monoidal categories and invariant theory.

Related

• Automorphism-invariant modules
• Irreducible morphisms and locally finite dimensional representations
• Infinite dimensional representations of canonical algebras
• From Morphism Categories to Functor Categories
• Covering theory, (mono)morphism categories and stable Auslander algebras