In this article, using the definitions of central series and nilpotency in the Lie algebras, we give some results similar to the works of Hulse and Lennox in 1976 and Hekster in 1986. Finally we will prove that every non trivial ideal of a nilpotent Lie algebra nontrivially intersects with the centre of Lie algebra, which is similar to Philip Hall's result in the group theory.

Multisoliton manifolds are characterized as symplectic prime ideals of the symplectic Lie algebra module generated by symmetries and mastersymmetries. This identification allows an explicit construction of the tangent bundle of the multisoliton manifolds.

in this paper, a useful classification of all lie subalgebras of a given lie algebraup to an inner automorphism is presented. this method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. after main results, we have applied this procedure for classifying the lie subalgebras of some examples of lie al...

Abstract We consider integrability structures of the generalized Hunter–Saxton equation. obtain Lax representation with non-removable spectral parameter, find local recursion operators for symmetries and cosymmetries, generate an infinite-dimensional Lie algebra higher symmetries, prove existence infinite number cosymmetries order. Further, we give examples employing order to constructing exact...

The presence of a (Lie-point) symmetry for a differential equation leads naturally to the useful notions of symmetric sets of solutions, i.e. of sets which are mapped into themselves by the symmetry, and of orbits of solutions. We introduce the definition of partial symmetry, and show that the above notions may be preserved, although the symmetry is not exact. We consider the quite exceptional ...

Some Lie algebra analogues of Schur's theorem and its converses are presented. As a result, it is shown that for a capable Lie algebra L we always have dim L=Z(L) 2(dim(L2))2. We also give give some examples sup- porting our results.

We consider two new classes of twisted D=4 quantum Poincaré symmetries described as the dual pairs of noncocommutative Hopf algebras. Firstly we investigate the two-parameter class of twisted Poincaré algebras which provide the Liealgebraic noncommutativity of the translations. The corresponding star-products and new deformed Lie-algebraic Minkowski spaces are introduced. We discuss further the...

It is shown for a simple ODE that it has many symmetry groups beyond its usual Lie group symmetries, when its generalized solutions are considered within the nowhere dense differential algebra of generalized functions. 0. Idea and Motivation The standard Lie group theory applied to symmetries of solutions of PDEs, Olver [1-3], deals with classical, and specifically, C-smooth solutions of such e...