一元根倾斜多项式代数上分级模块类别的组合学

Akihiro Higashitani, Kenta Ueyama
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引用次数: 0

摘要

我们引入了一种关于$\mathbb{Z}/\ellmathbb{Z}$上的偏斜对称矩阵的运算,称为切换,并定义了一类在$\mathbb{Z}/\ellmathbb{Z}$上的偏斜对称矩阵,称为模态尤勒矩阵。然后,我们证明这些矩阵与在$\ell$-th同根上的偏斜多项式数组上的分级模块类别密切相关。作为应用,我们研究了在立方根上的倾斜多项式代数的点简单复数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Combinatorics of graded module categories over skew polynomial algebras at roots of unity
We introduce an operation on skew-symmetric matrices over $\mathbb{Z}/\ell\mathbb{Z}$ called switching, and also define a class of skew-symmetric matrices over $\mathbb{Z}/\ell\mathbb{Z}$ referred to as modular Eulerian matrices. We then show that these are closely related to the graded module categories over skew polynomial algebras at $\ell$-th roots of unity. As an application, we study the point simplicial complexes of skew polynomial algebras at cube roots of unity.
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