Related papers: Ordinary differential equations described by their…
The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the…
We define an abstract framework called {\it discrete finite differences embedding} which can be used to obtain discrete analogue of formal functional relations in the spirit of category theory. For ordinary differential equations we exhibit…
It is known that the category of Lie algebras over a ring admits algebraic exponents. The aim of this paper is to show that the same is true for the category of internal Lie algebras in an additive, cocomplete, symmetric, closed, monoidal…
In this paper we study the general group classification of systems of linear second-order ordinary differential equations inspired from earlier works and recent results on the group classification of such systems. Some interesting results…
A Lie system is a system of first-order ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of vector fields: a so-called Vessiot-Guldberg Lie…
Two essential methods, the symmetry analysis and of the singularity analysis, for the study of the integrability of nonlinear ordinary differential equations are discussed. The main similarities and differences of these two different…
We exhibit a natural Lie algebra structure on the graded space of cyclic coinvariants of a symplectic vector space.
Some features of Cayley algebras (or algebras of octonions) and their Lie algebras of derivations over fields of low characteristic are presented. More specifically, over fields of characteristic $7$, explicit embeddings of any twisted form…
Let $\mathbb{K}$ be a field, $R$ be an associative and commutative $\mathbb{K}$-algebra and $L$ be a Lie algebra over $\mathbb{K}$. We give some descriptions of injections from $L$ to Lie algebra of $\mathbb{K}$-derivations of $R$ in the…
Singular perturbation theory plays a central role in the approximate solution of nonlinear differential equations. However, applying these methods is a subtle art owing to the lack of globally applicable algorithms. Inspired by the fact…
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.
The Lagrange problem is established in the discrete field theory subject to constraints with values in a Lie group. For the admissible sections that satisfy a certain regularity condition, we prove that the critical sections of such…
We discuss the effective computation of geometric singularities of implicit ordinary differential equations over the real numbers using methods from logic. Via the Vessiot theory of differential equations, geometric singularities can be…
The main definitions and properties of Lie superalgebras are proposed a la facon de a short dictionary, the different items following the alphabetical order. The main topics deal with the structure of simple Lie superalgebras and their…
We completely characterize cosymplectic and $\alpha$-cosymplectic Lie algebras in terms of corresponding symplectic Lie algebras and suitable derivations on them. Several examples are given and classification results are obtained in…
The normal form for a system of ode's is constructed from its polynomial symmetries of the linear part of the system, which is assumed to be semi-simple. The symmetries are shown to have a simple structure such as invariant function times…
For semisimple Lie superalgebras over an algebraically closed field of characteristic zero, whose category of finite dimensional super representations is semisismple, we classify all irreducible super representations for which the…
Discrete differential equations appear most prominently in planar map and lattice path enumeration. In this work we consider discrete differential equations with an additional parameter $x$, where the order of the equation is $1$ for $x=0$…
We show that all Lie point symmetries of various classes of nonlinear differential equations involving critical nonlinearities are variational/divergence symmetries.
We study and classify kinematical algebras which appear in the framework of Lie superalgebras or Lie algebras of order three. All these algebras are related through generalised Inon\"u-Wigner contractions from either the orthosymplectic…