Lie symmetry analysis of differential equations provides a powerful and fundamental framework to the exploitation of systematic procedures leading to the integration by quadrature (or at least to lowering the order) of ordinary differential equations, to the determination of invariant solutions of initial and boundary value problems, to the derivation of conservation laws, to the construction o...

Let A be a unital algebra and M be a unital A-bimodule. A characterization of generalized derivations and generalized Jordan derivations from A into M, through zero products or zero Jordan products, is given. Suppose that M is a unital left A-module. It is investigated when a linear mapping from A into M is a Jordan left derivation under certain conditions. It is also studied whether an algebra...

Working at the level of Poisson brackets, we describe the extension of the generalized Wakimoto realization of a simple Lie algebra valued current, J, to a corresponding realization of a group valued chiral primary field, b, that has diagonal monodromy and satisfies Kb ′ = Jb. The chiral WZNW field b is subject to a monodromy dependent exchange algebra, whose derivation is reviewed, too.

The phase space of theWess-Zumino-Witten model on a circle with target space a compact, connected, semisimple Lie group G is defined and the corresponding symplectic form is given. We present a careful derivation of the Poisson brackets of the Wess-Zumino-Witten model. We also study the canonical structure of the supersymmetric and the gauged Wess-Zumino-Witten models.

We study the Lie point symmetries and similarity transformations for partial differential equations of nonlinear one-dimensional magnetohydrodynamic system with Hall term known as HMHD system. For this 1+1 we find that is invariant under action a seventh dimensional algebra. Furthermore, optimal derived while invariants are applied derivation transformations. present different kinds oscillating...

We establish results about the second cohomology with coefficients in trivial module, symmetric invariant bilinear forms and derivations of a Lie algebra extended over commutative associative without unit. These provide simple unified approach to number questions treated earlier completely separated ways: periodization semisimple algebras (Anna Larsson), derivation algebras, prescribed part, ni...

Let R be a commutative ring with identity. By a Bres̃ar generalized derivation of R we mean an additive map g : R→ R such that g (xy) = g (x) y + xd (y) for all x, y ∈ R, where d is a derivation of R. And an additive mapping f : R → R is called a generalized derivation in the sense of Nakajima if it satisfies f(xy) = f(x)y + xf(y) − xf(1)y for all x, y ∈ R. In this paper we extend some results o...

We define the Poisson quasi-Nijenhuis structures with background on Lie algebroids and we prove that to any generalized complex structure on a Courant algebroid which is the double of a Lie algebroid is associated such a structure. We prove that any Lie algebroid with a Poisson quasi-Nijenhuis structure with background constitutes, with its dual, a quasi-Lie bialgebroid. We also prove that any ...

We give a constructive account of the fundamental ingredients of Poisson Lie theory as the basis for a description of the classical double group D. The double of a group G has a pointwise decomposition D ∼ G × G * , where G and G * are Lie subgroups generated by dual Lie algebras which form a Lie bialgebra. The double is an example of a factorisable Poisson Lie group, in the sense of Reshetikhi...