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

Autor:	Higashitani, Akihiro, Ueyama, Kenta
Rok vydání:	2024
Předmět:	Mathematics - Rings and Algebras Mathematics - Combinatorics Mathematics - Representation Theory
Druh dokumentu:	Working Paper
Popis:	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. Comment: v1: 16 pages; v2: 17 pages, added Example 4.10; v3: minor updates
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.10904 Zobrazit plný text záznamu View this record from Arxiv