Commutators of Pre-Lie n -Algebras and PL ∞ -Algebras

Mengjun Wang and Zhixiang Wu ()
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Mengjun Wang: School of Mathematical Sciences, Nanjing University, Nanjing, 210008, China
Zhixiang Wu: School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China

Mathematics, 2025, vol. 13, issue 11, 1-24

Abstract: We show that a P L ∞ -algebra V can be described by a nilpotent coderivation of degree − 1 on coalgebra P * V . Based on this result, we can generalise the result of Lada to show that every A ∞ -algebra carries a P L ∞ -algebra structure and every P L ∞ -algebra carries an L ∞ -algebra structure. In particular, we obtain a pre-Lie n -algebra structure on an arbitrary partially associative n -algebra and deduce that pre-Lie n -algebras are n -Lie admissible.

Keywords: n -ary algebras; pre-Lie algebras; left-symmetric algebras; L ∞ -algebras; A ∞ -algebras; PL ∞ -algebras; homotopy algebras; commutators; pre-Lie n -algebras (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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