Representations of a class of positively based algebras

We investigate the representation theory of the positively based algebra Am,d, which is a generalization of the noncommutative Green algebra of weak Hopf algebra corresponding to the generalized Taft algebra. It turns out that Am,d is of finite representative type if d ⩽ 4, of tame type if d = 5, and of wild type if d ⩾ 6. In the case when d ⩽ 4, all indecomposable representations of Am,d are constructed. Furthermore, their right cell representations as well as left cell representations of Am,d are described.