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

Akihiro Higashitani; Kenta Ueyama

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arxiv 2409.10904 v4 pith:ZQJQDZ5V submitted 2024-09-17 math.RA math.COmath.RT

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

Akihiro Higashitani , Kenta Ueyama This is my paper

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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.

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

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