The paper aims to construct nonlocal PT-symmetric integrable equations of fourth-order, from reductions a fourth-order system associated with the Lie algebra so(3,R). nonlocalities involved are reverse-space, reverse-time, and reverse-spacetime. All resulting possess infinitely many symmetries conservation laws.

The algebraic properties of drift-flux two-phase fluids models without gravitational and wall friction forces are studied. More precisely, for the two we consider equation states polytropic gases. We perform a classification scheme unknown parameters model such that to determine all possible admitted Lie symmetries. find in most general case dynamical system hyperbolic equations is invariant un...

A recent study (Muriel and Romero (2010a)) on the linearization of ordinary differential equations through generalized Sundman transformations suggests considering the problem of linearization through nonlocal transformations from the point of view of the λ−symmetries admitted by the equation and their associated first integrals. The systematic methods to calculate λ−symmetries and associated f...

This paper describes a new symmetry-based approach to solving a given ordinary di¬erence equation. By studying the local structure of the set of solutions, we derive a systematic method for determining one-parameter Lie groups of symmetries in closed form. Such groups can be used to achieve successive reductions of order. If there are enough symmetries, the di¬erence equation can be completely ...

We consider quantum dynamical systems whose degrees of freedom are described by N × N matrices, in the planar limit N → ∞. Examples are gauge theories and the M(atrix)-theory of strings. States invariant under U(N) are 'closed strings', modelled by traces of products of matrices. We have discovered that the U(N)-invariant operators acting on both open and closed string states form a remarkable ...

According to the Ringel-Green Theorem([G],[R1]), the generic composition algebra of the Hall algebra provides a realization of the positive part of the quantum group. Furthermore, the Drinfeld double of the generic composition algebra can be identified with the whole quantum group([X],[XY]), in which the BGP-reflection functors coincide with Lusztig’s symmetries. We first assert the elements co...

let $mathfrak{l}$ be the virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. we investigate the structure of the lie triplederivation algebra of $mathfrak{l}$ and $mathfrak{g}$. we provethat they are both isomorphic to $mathfrak{l}$, which provides twoexamples of invariance under triple derivation.

in this paper, by using of frobenius theorem a relation between lie subalgebras of the lie algebra of a top space t and lie subgroups of t(as a lie group) is determined. as a result we can consider these spaces by their lie algebras. we show that a top space with the finite number of identity elements is a c^{∞} principal fiber bundle, by this method we can characterize top spaces.