Commutators of pre Lie n-algebras and PL_∞-algebras

2021/07/28 by Mengjun Wang, Zhixiang Wu, Wang, Mengjun +1
Mathematics · Medicine · #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders

paper · pdf · doi:10.48550/arxiv.2107.13414

Abstract

We show that a PL_∞-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_∞-algebra carries a PL_∞-algebra structure and every PL_∞-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 pre Lie n-algebras are n-Lie admissible.

Related

• Pre-Lie algebras, their multiplicative lattice, and idempotent endomorphisms
• Commutative Post-Lie algebra structures on nilpotent Lie algebras and Poisson algebras
• L_∞ algebra structures of Lie algebra deformations
• Constructions of L_∞ algebras and their field theory realizations
• Pre-Lie algebras up to homotopy with divided powers and homotopy of operadic mapping spaces