计算量子平面上的各种模块

Q3 Mathematics

Algebraic Combinatorics Pub Date : 2021-10-29 DOI:10.5802/alco.230

Yifeng Huang

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引用次数: 1

摘要

设ζ是具有q个元素的有限域Fq中的一个固定非零元素。在本文中，我们通过给出一个生成函数来计算Fq上满足AB=ζBA的n×n矩阵的对（A，B）的数量。这推广了Feit和Fine的一个计算交换矩阵对的生成函数。我们的结果也可以看作是量子平面xy=ζyx上各种模的点计数，其几何结构由Chen和Lu描述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Counting on the variety of modules over the quantum plane

Let ζ be a fixed nonzero element in a finite field Fq with q elements. In this article, we count the number of pairs (A,B) of n × n matrices over Fq satisfying AB = ζBA by giving a generating function. This generalizes a generating function of Feit and Fine that counts pairs of commuting matrices. Our result can be also viewed as the point count of the variety of modules over the quantum plane xy = ζyx, whose geometry was described by Chen and Lu.

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来源期刊

Algebraic Combinatorics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

51 weeks