From pre-Lie rings back to braces

2022/08/04 by Smoktunowicz, Agata
#17A65 #17D99 #20F18 #20F40 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2208.02535

Abstract

Let A be a brace of cardinality pⁿ where p>n+1 is prime, and ann(pⁱ) be the set of elements of additive order at most pⁱ in this brace. A pre-Lie ring related to the brace A/ann(p²) was constructed in [8]. We show that there is a formula dependent only on the additive group of the brace A which reverses the construction from [8]. As an application example it is shown that the brace A/ann(p⁴) is the group of flows of a left nilpotent pre-Lie algebra.

Related

• From braces to pre-Lie rings
• On pre-Lie rings related to some non-Lazard braces
• On some connections between braces and pre-Lie rings outside of the context of Lazard's correspondence
• Classification of braces of cardinality p⁴
• On the passage from finite braces to pre-Lie rings