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Keywords:
positively based algebra; indecomposable module; cell module
positively based algebra; indecomposable module; cell module
Summary:
We investigate the representation theory of the positively based algebra $A_{m,d}$, which is a generalization of the noncommutative Green algebra of weak Hopf algebra corresponding to the generalized Taft algebra. It turns out that $A_{m,d}$ is of finite representative type if $d\leq 4$, of tame type if $d=5$, and of wild type if $d\ge 6.$ In the case when $d\leq 4$, all indecomposable representations of $A_{m,d}$ are constructed. Furthermore, their right cell representations as well as left cell representations of $A_{m,d}$ are described.
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