EconPapers    
Economics at your fingertips  
 

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

Mengjun Wang and Zhixiang Wu ()
Additional contact information
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
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/11/1792/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/11/1792/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:11:p:1792-:d:1665892

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().

 
Page updated 2025-05-28
Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1792-:d:1665892