Nijenhuis operators and twisted O-operators on Nambu-Poisson algebras

2025/10/17 by Apurba Das, Das, Apurba, Fattoum Harrathi +3
Mathematics · #17A40 #17B38 #17B40 #17B63 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2510.15640

openalex publication_date 2025/10/17 · openalex created_date 2025/10/21 · openalex updated_date 2026/07/28

Abstract

A ternary Nambu-Poisson algebra (which we call a Nambu-Poisson algebra in the paper) is the underlying algebraic structure of Nambu-Poisson manifolds of order 3 that appeared in the generalized Hamiltonian mechanics. First, we consider the 2nd cohomology group of a Nambu-Poisson algebra with coefficients in a given representation. Next, we discuss suitable linear deformations of a Nambu-Poisson algebra and show that any such trivial deformation yields a Nijenhuis operator on it. To understand the deformed Nambu-Poisson algebra obtained from a Nijenhuis operator, we introduce a new algebraic structure, which we name NS-Nambu-Poisson algebras. Finally, we consider O-operators twisted by 2-cocycles and find their close relationships with NS-Nambu-Poisson algebras.

Citations

• Nijenhuis deformations of Poisson algebras and F-manifold algebras
• Twisted O-operators on 3-Lie algebras and 3-NS-Lie algebras
• Cohomology and deformations of O-operators on Hom-associative algebras
• Generalized NS-algebras
• Cohomology and deformations of twisted Rota-Baxter operators and NS-algebras
• Non-Commutative ternary Nambu-Poisson algebras and ternary Hom-Nambu-Poisson algebras
• n-Lie algebras

Related

• Nijenhuis deformations of Poisson algebras and F-manifold algebras
• Non-Commutative ternary Nambu-Poisson algebras and ternary Hom-Nambu-Poisson algebras
• Solving the Poisson Yang-Baxter equation via deformation-to-quasiclassical-limits
• Transposed Poisson Structures on Two Nambu 3-Lie Algebras
• Valuation method for Nambu-Poisson algebras