A new formula for Lazard’s correspondence for finite braces and pre-Lie algebras. (English) Zbl 1505.16066
In this paper a one-to-one correspondence between finite right nilpotent \(\mathbb{F}_p\)-braces and finite nilpotent pre-Lie algebras over the field \(\mathbb{F}_p\) is established. The passage from braces to pre-Lie algebras is realized by a simple algebraic formula. This correspondence agrees with the one suggested by W. Rump [Note Mat. 34, No. 1, 115–145 (2014; Zbl 1344.14029)] by means of Lazard’s correspondence. As an application the author classifies all right nilpotent \(\mathbb{F}_p\)-braces generated by one element of cardinality \(p^4\).
Reviewer: Teresa Crespo (Barcelona)
MSC:
| 16Y99 | Generalizations |
| 16T25 | Yang-Baxter equations |
| 17A65 | Radical theory (nonassociative rings and algebras) |
| 17B99 | Lie algebras and Lie superalgebras |
Citations:
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