Abelian length categories of strongly unbounded type

TL;DR

This paper explores the concept of strongly unbounded type in abelian length categories, linking it to the Second Brauer-Thrall Conjecture for artin algebras, and introduces the space of characters as a new tool.

Contribution

It introduces the notion of strongly unbounded type for abelian length categories and connects it with the space of characters, providing new insights into the conjecture.

Findings

Establishes a relationship between strongly unbounded type and the Second Brauer-Thrall Conjecture

Utilizes the space of characters to analyze abelian length categories

Provides new theoretical tools for understanding representation types

Abstract

We discuss the notion of strongly unbounded type for abelian length categories; this is closely related to the Second Brauer-Thrall Conjecture for artin algebras. A new ingredient is the space of characters in the sense of Crawley-Boevey.