On the embedding of left-symmetric algebras into differential perm-algebras

P. S. Kolesnikov; B. K. Sartayev

On the embedding of left-symmetric algebras into differential perm-algebras

Rings and Algebras 2021-06-02 v1

Authors: P. S. Kolesnikov , B. K. Sartayev

Abstract

Given an associative algebra satisfying the left commutativity identity $abc=bac$ (Perm-algebra) with a derivation $d$ , the new operation $a\circ b = a d(b)$ is left-symmetric (pre-Lie). We derive necessary and sufficient conditions for a left-symmetric algebra to be embeddable into a differential Perm-algebra.

Keywords

left-symmetric algebra perm-algebra derivation pre-lie algebra embedding necessary and sufficient conditions

Cite

@article{arxiv.2106.00367,
  title  = {On the embedding of left-symmetric algebras into differential perm-algebras},
  author = {P. S. Kolesnikov and B. K. Sartayev},
  journal= {arXiv preprint arXiv:2106.00367},
  year   = {2021}
}

Comments

19 pages

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