Frölicher-Nijenhuis bracket and derived bracket associated to a nonsymmetric operad with multiplication

2025/05/04 by Baishya, Anusuiya, Das, Apurba
#16E40 #16W99 #17B70 #18M65 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2505.02044

Abstract

This paper aims to construct two graded Lie algebras associated with a nonsymmetric operad with multiplication. Maurer-Cartan elements of these graded Lie algebras correspond respectively to Nijenhuis elements and Rota-Baxter elements for the given multiplication. Explicit forms of these brackets are given to study Nijenhuis operators and Rota-Baxter operators on some Loday-type algebras.

Citations

• Controlling structures, deformations and homotopy theory for averaging algebras
• Gerstenhaber algebra of an associative conformal algebra
• Cohomology and deformations of O-operators on Hom-associative algebras
• Deformations of associative Rota-Baxter operators
• Deformations of Loday-type algebras and their morphisms
• Averaging algebras, Schröder numbers, rooted trees and operads
• On quadri-algebras
• Ennea-algebras

Related

• Cup product, Frölicher-Nijenhuis bracket and the derived bracket associated to Hom-Lie algebras
• Classical Yang-Baxter equations and Nijenhuis operators for Lie algebras
• Twisting on associative algebras and Rota-Baxter type operators
• Rota-Baxter operators and related structures on anti-flexible algebras
• Lie and Nijenhuis brackets on affine spaces