Commutators of pre Lie $n$-algebras and $PL_{\infty}$-algebras

Mengjun Wang; Zhixiang Wu

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arXiv · 2107.13414

Commutators of pre Lie $n$-algebras and $PL_{\infty}$-algebras

Mengjun Wang·Zhixiang Wu

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Abstract

We show that a $PL_{\infty}$-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 T. Lada and show that every $A_{\infty}$-algebra carries a $PL_{\infty}$-algebra structure and every $PL_{\infty}$-algebra carries an $L_{\infty}$-algebra structure. In particular, we obtain a pre Lie $n$-algebra structure on an arbitrary partially associative $n$-algebra and deduce pre Lie $n$-algebras are $n$-Lie admissible.

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BibTeX RIS

Mengjun Wang, Zhixiang Wu. 2021-07-28. Commutators of pre Lie $n$-algebras and $PL_{\infty}$-algebras. https://arxiv.org/abs/2107.13414

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