An embedding theorem for Nijenhuis Lie algebras

2025/12/11 by Najafizadeh, Alireza, Zargeh, Chia
#13P10 #16Z10 #17A50 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2512.10743

Abstract

This paper introduces the Higman-Neumann-Neumann extension (HNN extension; for short) for Nijenhuis Lie algebras and provides an embedding theorem. To this end, we employ the theory of Gröbner-Shirshov basis for Lie Ω-algebras in order to find a normal form for our construction. Then we show that every Nijenhuis Lie algebra embeds into its HNN-extension. Nijenhuis Lie algebras, Gröbner-Shirshov basis, HNN extension

Citations

• Cohomology, Homotopy, Extensions, and Automorphisms of Nijenhuis Lie Conformal Algebras
• Classical Yang-Baxter equations and Nijenhuis operators for Lie algebras
• Cohomology theory of Nijenhuis Lie algebras and (generic) Nijenhuis Lie bialgebras
• Nijenhuis operators on Leibniz algebras
• Operadic approach to HNN-extensions of Leibniz algebras
• HNN-extension of involutive multiplicative Hom-Lie algebras
• Existentially closed Leibniz algebras and an embedding theorem
• A Normal form for HNN-extension of Dialgebras
• Existentially closed structures and some embedding theorems

Related

• Classical Yang-Baxter equations and Nijenhuis operators for Lie algebras
• Operadic approach to HNN-extensions of Leibniz algebras
• HNN-extension of involutive multiplicative Hom-Lie algebras
• Gröbner-Shirshov bases for Lie Ω-algebras and free Rota-Baxter Lie algebras
• HNN extensions of Lie superalgebras