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