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首页> 外文期刊>Journal of algebra and its applications >Tilting mutation for m-replicated algebras
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Tilting mutation for m-replicated algebras

机译:m复制代数的倾斜突变

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Let A be a finite-dimensional hereditary algebra over an algebraically closed field k, m(A)be the m-replicated algebra of A and &mathscr m(A)$ be the m-cluster category of A. In this paper, we introduce the notion of mutation team in mod A ~((m)), and prove that each faithful almost complete tilting module over A ~((m)) has a mutation team by showing that the sequence of the complements satisfies the properties of the mutation team. We also prove that for each partial mutation team in the m-left part of mod A ~((m)), there exists a faithful almost complete tilting module having the partial mutation team as the set of indecomposable complements. As an application, we prove that m-cluster mutation in &mathscr m(A)can be realized as tilting mutation in mod A ~((m)), and we also give the relationship between connecting sequences in mod A(mand higher AR-angles in the m-cluster category &mathscr m(A).
机译:设A是代数封闭域k上的有限维遗传代数,m(A)是A的m复制代数,而m(A)$是A的m簇类别。在本文中,我们介绍mod A〜((m))中的突变团队的概念,并通过证明补体序列满足突变的性质,证明A〜((m))上每个忠实的几乎完整的倾斜模块都有一个突变团队球队。我们还证明,对于mod A〜((m))的m左部分中的每个部分突变组,存在一个忠实的,几乎完整的倾斜模块,该模块具有部分突变组作为不可分解的补集。作为一种应用,我们证明了可以将&mathscr m(A)中的m-cluster突变实现为mod A〜((m))中的倾斜突变,并且还给出了mod A中的连接序列之间的关系(要求更高的AR- m群集类别中的夹角&mathcr m(A)。

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