Puljić, Dora, Smoktunowicz, Agata and Nejabati Zenouz, Kayvan ORCID: 0000-0003-3285-9410 (2022) Some braces of cardinality p4 and related Hopf-Galois extensions. New York Journal of Mathematics, 28. pp. 494-522. ISSN 1076-9803

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Abstract

We describe all Fp-braces of cardinality p4 which are not
right nilpotent. The constructed braces are solvable and prime and
contain a non-zero strongly nilpotent ideal. We use the constructed
braces to construct examples of finitely dimensional pre-Lie algebras
which are left nilpotent but not right nilpotent. We also explain some
well known results about the correspondence between braces and Hopf-Galois extensions using the notion of Hopf-Galois extensions associated to a given brace. This can be applied to the constructed Fp-braces.

Item Type:	Article
Uncontrolled Keywords:	braces; Hopf-Galois extensions
Subjects:	Q Science > QA Mathematics
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science Faculty of Engineering & Science > School of Computing & Mathematical Sciences (CMS)
Related URLs:	Publisher Publisher
Last Modified:	20 May 2022 12:29
URI:	http://gala.gre.ac.uk/id/eprint/36302

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