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arXiv · 2409.10904

Combinatorics of graded module categories over skew polynomial algebras at roots of unity

Akihiro Higashitani·Kenta Ueyama
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Abstract

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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Akihiro Higashitani, Kenta Ueyama. 2024-09-17. Combinatorics of graded module categories over skew polynomial algebras at roots of unity. https://arxiv.org/abs/2409.10904

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