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On maximal green sequences in abelian length categories
Journal of Algebra ( IF 0.9 ) Pub Date : 2021-04-20 , DOI: 10.1016/j.jalgebra.2021.03.036
Siyang Liu , Fang Li

In this article, we study the relationship among maximal green sequences, complete forward hom-orthogonal sequences and stability functions in abelian length categories. Mainly, we firstly give a one-to-one correspondence between maximal green sequences and complete forward hom-orthogonal sequences via mutual constructions, and then prove that a maximal green sequence can be induced by a central charge if and only if it satisfies crossing inequalities. As applications, we show that crossing inequalities can be computed by c-vectors for finite dimensional algebras; finally, we give the Rotation Lemma for finite dimensional Jacobian algebras.



中文翻译:

关于阿贝尔长度类别中的最大绿色序列

在本文中,我们研究了最大绿色序列,完整正向正交序列和阿贝尔长度类别中的稳定性函数之间的关系。首先,我们首先通过相互构造给出最大绿色序列与完整的正向正交序列之间的一一对应关系,然后证明只要且仅当满足交叉不等式时,中心电荷才能诱导出最大绿色序列。 。作为应用,我们证明了对于有限维代数,交叉不等式可以通过c-矢量来计算。最后,给出有限维雅可比代数的旋转引理。

更新日期:2021-04-21
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