Coil enlargements of algebras

Abstract

Let $A$ be a finite dimensional, basic and connected algebra over an algebraically closed field $k$. We define a notion of weakly separating family in the Auslander-Reiten quiver of $A$ which generalises the notion of a separating tubular family introduced by C. M. Ringel. Given an algebra $A$ having a weakly separating family $\mathcal{F}$ of stable tubes, we say that an algebra $B$ is a coil enlargement of $A$ using modules from $\mathcal{F}$ if $B$ is obtained from $A$ by an iteration of admissible operations performed either on a stable tube of $\mathcal{F}$, or on a coil obtained from a stable tube of $\mathcal{F}$ by means of the operations done so far. The purpose of this paper is to describe the module category of $B$. We also give a criterion for the tameness of $B$ if $A$ is a tame concealed algebra.