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Abstract / Description of output
In this paper a simple algebraic formula is obtained for the correspondence between finite right nilpotent Fpbraces and finite nilpotent preLie algebras. This correspondence agrees with the correspondence using Lazard's correspondence between finite Fpbraces and preLie algebras proposed by Wolfgang Rump in 2014. As an application example, a classification of all right nilpotent Fpbraces 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.
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 language  English 

Number of pages  24 
Journal  Journal of Algebra 
Publication status  Accepted/In press  7 Dec 2021 
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Quantum integrability from set theoretic YangBaxter & reflection equations
1/10/21 → 30/09/24
Project: Research

Enhancing Representation Theory, Noncommutative Algebra And Geometry Through Moduli, Stability And Deformations
Gordon, I., Bayer, A. & Smoktunowicz, A.
1/05/18 → 30/04/24
Project: Research