Skew braces and Hopf-Galois structures of Heisenberg type

被引：24
|
作者：
Zenouz, Kayvan Nejabati [1 ]
机构：
[1] Oxford Brookes Univ, Sch Engn Comp & Math, Oxford OX33 1HX, England
来源：
JOURNAL OF ALGEBRA | 2019年 / 524卷
基金：
英国工程与自然科学研究理事会;
关键词：
Skew braces; Hopf-Galois structures; Heisenberg group; Field extensions; The Yang-Baxter equation; FIELD-EXTENSIONS; CLASSIFICATION;
D O I：
10.1016/j.jalgebra.2019.01.012
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We classify all skew braces of Heisenberg type for a prime number p > 3. Furthermore, we determine the automorphism group of each one of these skew braces (as well as their socle and annihilator). Hence, by utilising a link between skew braces and Hopf-Galois theory, we can determine all Hopf-Galois structures of Heisenberg type on Galois field extensions of fields of degree p(3). Crown Copyright (C) 2019 Published by Elsevier Inc. All rights reserved.
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页码：187 / 225
页数：39
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