Twisted group algebra of dihedral groups over finite fields

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2026-06-01 Epub Date: 2026-01-13 DOI:10.1016/j.ffa.2026.102792

André Duarte

引用次数: 0

Abstract

Let

F_{q}

be a finite field and

D_{n}

is the dihedral group of order 2n. We present formulas for a complete set of 2-cocycles of

D_{n}

over

F_{q}

and compute the primitive central idempotents of

F_{q}^{α} D_{n}

. We conclude by describing the Wedderburn decomposition of

F_{q}^{α} D_{n}

and the irreducible projective representations of

D_{n}

over

F_{q}

查看原文本刊更多论文

有限域上二面体群的扭曲群代数

设Fq是一个有限域，Dn是2n阶的二面体群。我们给出了Dn / Fq的2环完备集的公式，并计算了FqαDn的原始中心幂等。最后，我们描述了FqαDn的Wedderburn分解和Dn / Fq的不可约投影表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.