Tree modules

TL;DR

This paper introduces methods to construct indecomposable tree modules for all roots in quivers without oriented cycles, providing a comprehensive approach for building such modules and illustrating the process with examples.

Contribution

It develops a general recipe for constructing indecomposable tree modules for every root, extending previous tools to all imaginary Schur roots.

Findings

Constructed indecomposable tree modules for all imaginary Schur roots.

Provided a systematic construction method applicable to all roots.

Included illustrative examples demonstrating the methods.

Abstract

After stating several tools which can be used to construct indecomposable tree modules for quivers without oriented cycles, we use these methods to construct indecomposable tree modules for every imaginary Schur root. These methods also give a recipe for the construction of tree modules for every root. Moreover, we give several examples illustrating the results.