On regular irreducible components of module varieties over string algebras

TL;DR

This paper characterizes the regular irreducible components of module varieties over string algebras, expanding the understanding of algebraic structures beyond well-studied classes like hereditary and tubular algebras.

Contribution

It provides the first detailed description of irreducible components for module varieties over string algebras, a significant step beyond classical algebra types.

Findings

Identifies regular irreducible components for mod(A,d) over string algebras

Extends the classification of module varieties beyond hereditary and tubular cases

Offers new insights into the structure of string algebra representations

Abstract

We determine the regular irreducible components of the variety mod(A,d), where A=kQ/I is a string algebra and I is generated by a set of paths of length two. Our case is among the first examples of descriptions of irreducible components, aside from hereditary, tubular and Gelfand-Ponomarev algebras.