A multiplication formula for module subcategories of Ext-symmetry

TL;DR

This paper introduces evaluation forms for modules in a subcategory of Ext-symmetry over a path algebra, establishing a multiplication formula similar to that for preprojective algebra modules, advancing understanding of module interactions.

Contribution

It defines evaluation forms in Ext-symmetric subcategories and proves a new multiplication formula analogous to known results for preprojective algebras.

Findings

Established evaluation forms for modules in Ext-symmetric subcategories.

Proved a multiplication formula for these evaluation forms.

Connected the new formula to existing results in preprojective algebra theory.

Abstract

We define evaluation forms associated to objects in a module subcategory of Ext-symmetry generated by finitely many simple modules over a path algebra with relations and prove a multiplication formula for the product of two evaluation forms. It is analogous to a multiplication formula for the product of two evaluation forms associated to modules over a preprojective algebra given by Geiss, Leclerc and Schr\"oer in \cite{GLS2006}.