On the passage from finite braces to pre-Lie rings

Agata Smoktunowicz

On the passage from finite braces to pre-Lie rings

Rings and Algebras 2022-04-29 v3

Authors: Agata Smoktunowicz

Abstract

Let p be a prime number. We show that there is a one-to-one correspondence between the set of strongly nilpotent braces and the set of nilpotent pre-Lie rings of cardinality $p^{n}$ , for sufficiently large p. Moreover, there is an injective mapping from the set of left nilpotent pre-Lie rings into the set of left nilpotent braces of cardinality $p^{n}$ for n+1<p. For the passage from pre-Lie rings to braces we use exactly the same method as suggested in [41].

Keywords

finite brace pre-lie ring strongly nilpotent left nilpotent one-to-one correspondence injective mapping

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@article{arxiv.2202.00085,
  title  = {On the passage from finite braces to pre-Lie rings},
  author = {Agata Smoktunowicz},
  journal= {arXiv preprint arXiv:2202.00085},
  year   = {2022}
}

Comments

arXiv admin note: text overlap with arXiv:2011.07611 Some assumptions were removed from Lemma 15 answering Question 3, also Question 3 was removed.A gap in the proof of Theorem 2 was corrected

On the passage from finite braces to pre-Lie rings

Abstract

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