Related papers: On the Lie noncommutative integrability
The set of points of a one-dimensional cut-and-project quasicrystal or model set, while not additive, is shown to be multiplicative for appropriate choices of acceptance windows. This leads to the definition of an associative additive…
A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be…
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
In this paper, we classify eight-dimensional non-solvable Lie algebras that support a symplectic structure. As well as a complete classification is given, up to symplectomorphism, of eight-dimensional symplectic non-solvable Lie algebras.
We propose a new approach that allows one to reduce nonlinear equations on Lie groups to equations with a fewer number of independent variables for finding particular solutions of the nonlinear equations. The main idea is to apply the…
We present a formalization, in the theorem prover Lean, of the classification of solvable Lie algebras of dimension at most three over arbitrary fields. Lie algebras are algebraic objects which encode infinitesimal symmetries, and as such…
This thesis was concerned with classifying the real indecomposable solvable Lie algebras with codimension one nilradicals of dimensions two through seven. This thesis was organized into three chapters. In the first, we described the…
In this thesis new objects to the existing set of invariants of Lie algebras are added. These invariant characteristics are capable of describing the nilpotent parametric continuum of Lie algebras. The properties of these invariants, in…
A Lie system is the non-autonomous system of differential equations describing the integral curves of a non-autonomous vector field taking values in a finite-dimensional Lie algebra of vector fields, a so-called Vessiot--Guldberg Lie…
In this paper, we explain how to compute the Lie algebra of the differential Galois group of a reducible linear differential system. We achieve this by showing how to transform a block-triangular linear differential system into a…
A family of Lie algebras of minimal dimension associated with vector fields that define a non-linear dynamical system is calculated. These Lie algebras contain the Heinsenberg algebra. An element that distinguishes these vector fields is…
A new form of a binary Darboux transformation is used to generate analytical solutions of a nonlinear Liouville-von Neumann equation. General theory is illustrated by explicit examples.
This note presents a general theorem about the cohomology of finite dimensional Lie algebras of arbitrary characteristic. As an application we compute the cohomology of the Borel subalgebra of sl(N).
One of the four well-known series of simple Lie algebras of Cartan type is the series of Lie algebras of Special type, which are divergence-free Lie algebras associated with polynomial algebras and the operators of taking partial…
An infinite-dimensional Lie Algebra is proposed which includes, in its subalgebras and limits, most Lie Algebras routinely utilized in physics. It relies on the finite oscillator Lie group, and appears applicable to twisted noncommutative…
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…
We define a solvable extension of the graph 2-step nilpotent Lie algebras of [5] by adding elements corresponding to the 3-cliques of the graph. We study some of their basic properties and we prove that two such Lie algebras are isomorphic…
In this article, we described 1/2-derivations of solvable Lie algebras with a thread-like nilradical. Nontrivial transposed Poisson algebras with solvable Lie algebras are constructed. That is, by using 1/2-derivations of Lie algebras, we…
The present paper is the third contribution of a series of works, where we investigate pseudo--bosonic operators and their connections with finite dimensional Lie algebras. We show that all finite dimensional nilpotent Lie algebras (over…
We construct a new family of infinite-dimensional quasi-graded Lie algebras on hyperelliptic curves. We show that constructed algebras possess infinite number of invariant functions and admit a decomposition into the direct sum of two…