FROM BRACES TO PRE-LIE RINGS

Aner Shalev, Agata Smoktunowicz

Research output: Contribution to journalArticlepeer-review

Abstract

Let A be a brace of cardinality pn where p > n + 1 is prime and let ann(p2) be the set of elements of additive order at most p2 in this brace. We construct a pre-Lie ring related to the brace A/ann(p2). In the case of strongly nilpotent braces of nilpotency index k < p the brace A/ann(p2) can be recovered by applying the construction of the group of flows to the resulting pre-Lie ring. We do not know whether or not our construction is related to the group of flows when applied to braces which are not right nilpotent.

Original languageAmerican English
Pages (from-to)1545-1559
Number of pages15
JournalProceedings of the American Mathematical Society
Volume152
Issue number4
DOIs
StatePublished - 1 Apr 2024

Bibliographical note

Publisher Copyright:
© 2024 American Mathematical Society.

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