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Representations of a class of positively based algebras
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 3, pp. 811-838
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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.
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.
DOI : 10.21136/CMJ.2023.0254-22
Classification : 16D80, 16G60
Keywords: positively based algebra; indecomposable module; cell module 
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Lin, Shiyu; Yang, Shilin. Representations of a class of positively based algebras. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 3, pp. 811-838. doi: 10.21136/CMJ.2023.0254-22

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