Commutators of pre Lie $n$-algebras and $P{L}_{\infty }$-algebras

Mengjun Wang, Zhixiang Wu

We show that a $P{L}_{\infty }$-algebra $V$ can be described by a nilpotent coderivation of degree $-1$ on coalgebra $P^{\ast }V$. Based on this result, we can generalise the result of T. L…