In this paper, first we introduce the notion of a Reynolds operator on an n-Lie algebra and illustrate relationship between operators derivations algebra. We give cohomology theory study infinitesimal deformations using second group. Then NS-n-Lie algebras, which are generalizations both algebras n-pre-Lie algebras. show that gives rise to together with representation itself. Nijenhuis naturall...

In this paper we study the Lie algebras of derivations two-step nilpotent algebras. We obtain a class with trivial center and abelian ideal inner derivations. Among these, relations between complex real case indecomposable Heisenberg Leibniz are thoroughly described. Finally show that every almost derivation algebra one-dimensional commutator ideal, three exceptions, is an derivation.

The main goal of this paper is to introduce the notion 3-L-dendriform algebras which are dendriform version 3-pre-Lie algebras. In fact they algebraic structures behind O-operator They can be also regarded as ternary analogous L-dendriform Moreover, we study generalized derivations Finally, explore spaces quasi-derivations, centroids and quasi-centroids give some properties.

The central part of calculus on manifolds is usually the calculus of differential forms and the best known operators are exterior derivative, Lie derivatives, pullback and insertion operators. Differential forms are a graded commutative algebra and one may ask for the space of graded derivations of it. It was described by Frölicher and Nijenhuis in [1], who found that any such derivation is the...

The Lie algebra W = DerA is called the Witt algebra. It consists of “vector fields” f∂, f ∈ A. In particular, dimF W = dimF A = p. As any Lie algebra of derivations of a commutative algebra over F, W has a canonical structure of a restricted Lie algebra. Recall that a restricted Lie algebra is a Lie algebra over F with an additional unary (in general, non-linear) operation g 7→ g satisfying the...