## Tsukuba Journal of Mathematics

### 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.

#### Article information

Source
Tsukuba J. Math., Volume 19, Number 2 (1995), 453-479.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496162881

Digital Object Identifier
doi:10.21099/tkbjm/1496162881

Mathematical Reviews number (MathSciNet)
MR1366647

Zentralblatt MATH identifier
0860.16014

#### Citation

Assem, Ibrahim; Skowronski, Andrzej; Tome, Bertha. Coil enlargements of algebras. Tsukuba J. Math. 19 (1995), no. 2, 453--479. doi:10.21099/tkbjm/1496162881. https://projecteuclid.org/euclid.tkbjm/1496162881