A Multiplication Formula for Module Subcategories of Ext-symmetry

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 Schröer in [7]. Introduction Let Λ be the preprojective algebra associated to a connected quiver without loops (see e.g. [12]) and mod(Λ) be the category of finite-dimensional nilpotent left Λmodules. We denote by Λe the variety of finite-dimensional nilpotent left Λ-modules with dimension vector e. For any x ∈ Λe, there is an evaluation form δx associated to x satisfying that there is a finite subset R(e) of Λe such that Λe = ⊔ x∈R(e)〈x〉 where 〈x〉 := {y ∈ Λe | δx = δy} [7, Section 1.2]. Inspired by the Caldero-Keller cluster multiplication theorem for finite type [4], Geiss, Leclerc and Schröer [7] proved a multiplication formula (the Geiss-Leclerc-Schröer multiplication formula) as follows: χ(PExt Λ(x , x)) δx′⊕x′′ = ∑