A representation embedding for algebras of infinite type

Abstract

We show that for any finite-dimensional algebra Λ of infinite representation type, over a perfect field, there is a bounded principal ideal domain Γ and a representation embedding from $\Gamma \text{-}\mathrm{mod}$ into $\Lambda \text{-}\mathrm{mod}$. As an application, we prove a variation of the second Brauer-Thrall conjecture: finite-dimensional algebras of infinite-representation type admit infinite families of non-isomorphic finite-dimensional indecomposables with fixed endolength, for infinitely many endolengths.