Semilinear clannish algebras

TL;DR

This paper introduces semilinear clannish algebras, a new class generalizing clannish and string algebras, and classifies their finite-dimensional indecomposable modules.

Contribution

It defines semilinear clannish algebras and provides a classification of their finite-dimensional indecomposable modules, extending prior algebraic frameworks.

Findings

Classification of finite-dimensional indecomposable modules

Generalization of clannish and string algebras

Introduction of semilinear structure in algebra

Abstract

We define a class of associative algebras generalizing 'clannish algebras', as introduced by the second author, but also incorporating semilinear structure, like a skew polynomial ring. Clannish algebras generalize the well known 'string algebras' introduced by Butler and Ringel. Our main result is the classification of finite-dimensional indecomposable modules for these new algebras.