One class of representations over trivial extensions of iterated tilted algebras
The authors consider the following situation. Let \(k\) be an algebraically closed field and \(A\) be a finite dimensional iterated tilted algebra of type \(\vec{\Delta}\). Consider the trivial extension of \(A\), \(T(A) = A \bowtie D(A)\), where \(D\) denotes the usual duality \(\text{Hom}_ k(- ,k)\). The main results here concern \(T(A)\)-modules which belong to components of the Auslander-Reiten quiver of \(T(A)\) of the form \(\mathbb{Z} \vec{\Delta}\). Such modules are called modules on platform. They are not directing but enjoy very nice properties. To mention some of them: (i) 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; (ii) a module on platform is uniquely determined by its top and socle; (iii) a module on platform is uniquely determined by its Loewy factor and by its socle factor.
finite dimensional iterated tilted algebras
scientific article; zbMATH DE number 515578