Skew Braces and Hopf-Galois Structures of Heisenberg Type

2018/04/04 by Kayvan Nejabati Zenouz, Zenouz, Kayvan Nejabati
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1804.01360

openalex publication_date 2018/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 p³ .

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