A new formula for Lazard's correspondence for finite braces and pre-Lie algebras

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Abstract / Description of output

In this paper a simple algebraic formula is obtained for the correspondence between finite right nilpotent Fp-braces and finite nilpotent pre-Lie algebras. This correspondence agrees with the correspondence using Lazard's correspondence between finite Fp-braces and pre-Lie algebras proposed by Wolfgang Rump in 2014. As an application example, a classification of all right nilpotent Fp-braces generated by one element of cardinality p^4 is obtained, answering a question posed by Leandro Vendramin.
It is also shown that the sum of a finite number of left nilpotent ideals in a left brace is a left nilpotent ideal, therefore every finite brace contains the largest left nilpotent ideal.
Original languageEnglish
Number of pages24
JournalJournal of Algebra
Publication statusAccepted/In press - 7 Dec 2021

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