Skew braces and Hopf-Galois structures of Heisenberg type

JOURNAL OF ALGEBRA

卷:524

Article

Zenouz, Kayvan Nejabati¹ 

[1] Oxford Brookes Univ, Sch Engn Comp & Math, Oxford OX33 1HX, England

关键词: Skew braces;    Hopf-Galois structures;    Heisenberg group;    Field extensions;    The Yang-Baxter equation;   

DOI  :  10.1016/j.jalgebra.2019.01.012

来源: Elsevier

【 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.

【 授权许可】

Free