It is proved that the derivation algebra of a centerless perfect Lie algebra of arbitrary dimension over any field of arbitrary characteristic is complete and that the holomorph of a centerless perfect Lie algebra is complete if and only if its outer derivation algebra is centerless. Key works: Derivation, complete Lie algebra, holomorph of Lie algebra Mathematics Subject Classification (1991):...

We give the classification of solvable and splitting Lie triple systems and it turn that, up to isomorphism there exist 7 non isomorphic canonical Lie triple systems and, 6 non isomorphic splitting canonical Lie triple systems and find the solvable Lie algebras associated.

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...

The notion of a non-associative universal enveloping algebra for a Lie triple system arises when Lie triple systems are considered as Bol algebras (more generally, Sabinin algebras). In this paper a new construction for these universal enveloping algebras is given, and their properties are studied. It is shown that universal enveloping algebras of Lie triple systems have surprisingly few ideals...

A unital $C^*$ -- algebra $mathcal A,$ endowed withthe Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie$C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and$g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda Lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

Throughout this note, R will be always a prime ring of characteristic different from 2 with center Z(R), extended centroid C, and two-sided Martindale quotient ring Q. Let f : R→ R be additive mapping of R into itself. It is said to be a derivation of R if f (xy)= f (x)y + x f (y), for all x, y ∈ R. Let S⊆ R be any subset of R. If for any x, y ∈ S, f ([x, y])= [ f (x), y] + [x, f (y)], then the...