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

Author

Listed:
  • Mengjun Wang

    (School of Mathematical Sciences, Nanjing University, Nanjing, 210008, China)

  • Zhixiang Wu

    (School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China)

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.

Suggested Citation

  • Mengjun Wang & Zhixiang Wu, 2025. "Commutators of Pre-Lie n -Algebras and PL ∞ -Algebras," Mathematics, MDPI, vol. 13(11), pages 1-24, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1792-:d:1665892
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