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Skew braces and Hopf–Galois structures of Heisenberg type

Skew braces and Hopf–Galois structures of Heisenberg type

Nejabati Zenouz, Kayvan ORCID: 0000-0003-3285-9410 (2019) Skew braces and Hopf–Galois structures of Heisenberg type. Journal of Algebra, 524. pp. 187-225. ISSN 0021-8693 (doi:https://doi.org/10.1016/j.jalgebra.2019.01.012)

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Abstract

We classify all skew braces of Heisenberg type for a prime number p. 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.

Item Type: Article
Uncontrolled Keywords: skew braces, Hopf–Galois structures, Heisenberg group, field extensions, the Yang–Baxter equation
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Architecture, Computing & Humanities
Faculty of Architecture, Computing & Humanities > Department of Mathematical Sciences
Last Modified: 27 Aug 2019 08:56
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/24842

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