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The structure of the nonlinear Schrodinger prolongation algebra, introduced by Estabrook and Wahlquist, is explicitly determined. It is proved that this Lie algebra is isomorphic with the direct product Hx (A, @C[t]), where H is a three-dimensional commutative Lie algebra.

‎In this paper‎, ‎we introduce the structure of a groupoid associated to a vector field‎ ‎on a smooth manifold‎. ‎We show that in the case of the $1$-dimensional manifolds‎, ‎our‎ ‎groupoid has a‎ ‎smooth structure such that makes it into a Lie groupoid‎. ‎Using this approach‎, ‎we associated to‎ ‎every vector field an equivalence‎ ‎relation on the Lie algebra of all vector fields on the smooth...

A 3-graph is a connected cubic graph such that each vertex is is equipped with a cyclic order of the edges incident with it. A weight system is a function f on the collection of 3-graphs which is antisymmetric: f(H) = −f(G) if H arises from G by reversing the orientation at one of its vertices, and satisfies the IHX-equation. Key instances of weight systems are the functions φg obtained from a ...

‎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 ...

In these notes, we give a brief overview of the (finite dimensional) representation theory of finite dimensional semisimple Lie algebras. We first study the example of sl2(C) and then provide the general (additive) theory, along with an analysis of the representations of sl3(C). In the last section, we have a look at the multiplicative structure of the representation ring, discussing examples f...