One class of representations over trivial extensions of iterated tilted algebras

Abstract

Let $T(A)=A\ltimes D(A)$ be the trivial extension of iterated tilted algebra $A$ of type $\vec{\Delta}$. In this paper, we study the indecomposable $T(A)$-modules belonging to the components of form $Z\vec{\Delta}$, which are called the modules on platform. Our main results are as follows: (1) The number of the modules on platform which have the same dimension vector is equal to or less than the number of simple $A$-modules. (2) The module on platform is uniquely determined by its top and socle. (3) The module on platform is uniquely determined by its Loewy factor and by its socle factor.