‎In this paper Lie point symmetries‎, ‎Hamiltonian equations and conservation‎ ‎laws of general three-dimensional anisotropic non-linear sourceless heat transfer‎ ‎equation are investigated‎. ‎First of all Lie symmetries are obtained by using the general method‎ based on invariance condition of a system of differential equations under a pro‎longed vector field‎. ‎Then the structure of symmetry ...

We initiate the study of ξ-groups and Hu-Liu Leibniz algebras, claim that almost all simple Leibniz algebras and simple Hu-Liu Leibniz algebras are linear, and establish two passages. One is the passage from a special Z2-graded associative algebra to a Hu-Liu Leibniz algebra. The other one is the passage from a linear ξ-group to its tangent space which is a Hu-Liu Leibniz algebra. The Lie corre...

‎in this paper lie symmetry analysis is applied in order to find new solutions for fokker plank equation of ornstein-uhlenbeck process‎. ‎this analysis classifies the solutions format of the fokker plank equation by using the lie algebra of the symmetries of our considered stochastic process‎.

We interpret geometrically a variant of the Robinson-Schensted correspondence which links Brauer diagrams with updown tableaux, in the spirit of Steinberg’s result [32] on the original Robinson-Schensted correspondence. Our result uses the variety of all (N , ω, V) where V is a complete flag in C2n, ω is a nondegenerate alternating bilinear form on C2n, and N is a nilpotent element of the Lie a...

We identify the periodic cyclic homology of the algebra of complete symbols on a differential groupoid G in terms of the cohomology of S * (G), the cosphere bundle of A(G), where A(G) is the Lie algebroid of G. We also relate the Hochschild homology of this algebra with the homogeneous Poisson homology of the space A * (G) 0 ∼ = S * (G) × (0, ∞), the dual of A(G) with the zero section removed. ...

We prove the following theorem: Let K be a connected symmetric subgroup of the group of isometries of a compact connected globally Riemannian symmetric space M. Then, K acts in a variationally complete manner on M. (We refer to the work of R. Bott and H. Samelson [l; 2] for a definition of this concept and applications to topology.) Let G be a compact, connected Lie group, L a connected symmetr...

We study a certain class of non-maximal rank contractions of the nilpotent Lie algebra gm and show that these contractions are completable Lie algebras. As a consequence a family of solvable complete Lie algebras of non-maximal rank is given in arbitrary dimension. . AMS Math. Subj. Class. 17B10, 17B30.

A Riemannian Einstein solvmanifold (possibly, any noncompact homogeneous Einstein space) is almost completely determined by the nilradical of its Lie algebra. A nilpotent Lie algebra, which can serve as the nilradical of an Einstein metric solvable Lie algebra, is called an Einstein nilradical. Despite a substantial progress towards the understanding of Einstein nilradicals, there is still a la...