A new singular perturbation method based on the Lie symmetry group is presented to a system of difference equations. This method yields consistent derivation of a renormalization group equation which gives an asymptotic solution of the difference equation. The renormalization group equation is a Lie differential equation of a Lie group which leaves the system approximately invariant. For a 2-D ...

In one of our recent papers, the associative and the Lie algebras of Weyl type A[D] = A⊗IF [D] were defined and studied, where A is a commutative associative algebra with an identity element over a field IF of any characteristic, and IF [D] is the polynomial algebra of a commutative derivation subalgebra D of A. In the present paper, a class of the above associative and Lie algebras A[D] with I...

In this paper, we describe a geometric setting for higher-order lagrangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we deduce an intrinsic framework for this type of dynamical systems. Interesting applications as, for instance, a geometric derivation of the higher-order Euler-Po...

Several integration schemes exits to solve the equations of motion of the N -body problem. The Lie-integration method is based on the idea to solve ordinary differential equations with Lie-series. In the 1980s this method was applied for the N -body problem by giving the recurrence formula for the calculation of the Lie-terms. The aim of this works is to present the recurrence formulae for the ...

Let $R$ be a prime ring with its Utumi ring of quotients $U$,  $C=Z(U)$ the extended centroid of $R$, $L$ a non-central Lie ideal of $R$ and $0neq a in R$. If $R$ admits a generalized derivation $F$ such that $a(F(u^2)pm F(u)^{2})=0$ for all $u in L$, then one of the following holds: begin{enumerate} item there exists $b in U$ such that $F(x)=bx$ for all $x in R$, with $ab=0$; item $F(x)=...

In a recent paper by the authors, the associative and the Lie algebras of Weyl type A[D] = A⊗F[D] were introduced, where A is a commutative associative algebra with an identity element over a field F of any characteristic, and F[D] is the polynomial algebra of a commutative derivation subalgebra D of A. In the present paper, a class of the above associative and Lie algebras A[D] with F being a ...

Given an associative algebra satisfying the left commutativity identity abc = bac (Perm-algebra) with a derivation d, new operation a°b=ad(b) is left-symmetric (pre-Lie). We derive necessary and sufficient conditions for to be embeddable into differential Perm-algebra.

In this paper, we describe the derivations of complex n-dimensional naturally graded filiform Leibniz algebras NGF1, NGF2, and NGF3. We show that the dimension of the derivation algebras of NGF1 and NGF2 equals n+1 and n+2, respectively, while the dimension of the derivation algebra of NGF3 is equal to 2n−1. The second part of the paper deals with the description of the derivations of complex n...

In this paper, we investigate Jordan ?-derivations and Lie on path algebras. This work is motivated by the one of Benkovic done triangular algebras study derivations Li Wei. Namely, main results state that every ?-derivation a standard form algebra when associated quiver acyclic finite.