The geometry of uniserial representations of finite dimensional algebras III: Finite uniserial type

Abstract

A description is given of those sequences $\mathbb{S}=(S(0),S(1),\dots ,S(l))$ of simple modules over a finite dimensional algebra for which there are only finitely many uniserial modules with consecutive composition factors $S(0),\dots ,S(l)$. Necessary and sufficient conditions for an algebra to permit only a finite number of isomorphism types of uniserial modules are derived. The main tools in this investigation are the affine algebraic varieties parametrizing the uniserial modules with composition series $\mathbb{S}$.