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Representations of a class of positively based algebras. (English) Zbl 07729539

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.

MSC:

16D80 Other classes of modules and ideals in associative algebras
16G60 Representation type (finite, tame, wild, etc.) of associative algebras
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