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Rational Factorization of Hamiltonian Flows in the Space Dual to the Lie Algebra of Fractional Integrodifferential Operators and Benney-Type Integrable Hydrodynamic Systems
For the Lax-type Hamiltonian flows in the space dual to the Lie algebra of fractional integrodifferential operators, we develop a rational...
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Lie Bialgebroid of Pseudo-differential Operators
We associate a Lie bialgebroid structure to the algebra of formal Pseudo-differential operators, as the classical limit of a quantum groupoid. As a...
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Lie algebras of differential operators for matrix valued Laguerre type polynomials
We study algebras of differential and difference operators acting on matrix valued orthogonal polynomials (MVOPs) with respect to a weight matrix of...
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The Principal Symbol of Elliptic Differential Operators on Lie Groups and Homogeneous Spaces
We associate a principal symbol with elliptic differential operators acting on sections of vector fibrations over Lie groups and homogeneous spaces....
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Lie algebra classification, conservation laws and invariant solutions for the kind generalization of the Duffing-type equation
This paper makes significant contributions to the study of a generalized form of the Duffing-type equation. We derive the generating operators of the...
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DIFFERENTIAL GRADED LIE GROUPS AND THEIR DIFFERENTIAL GRADED LIE ALGEBRAS
In this paper we discuss the question of integrating differential graded Lie algebras (DGLA) to differential graded Lie groups (DGLG). We first...
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q-Poincaré Inequalities on Carnot Groups with Filiform Type Lie Algebra
In this paper we prove (global) q - Poincaré inequalities for probability measures on nilpotent Lie groups with filiform Lie algebra of any length....
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Lie Algebra Classification, Conservation Laws and Invariant Solutions for a Generalization of the Sharma–Tasso–Olever Equation
Sharma–Tasso–Olever equation is an interesting partial differential equation with multiple associated studies. This type of nonlinear evolution...
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Closure of the Laplace-Beltrami Operator on 2D Almost-Riemannian Manifolds and Semi-Fredholm Properties of Differential Operators on Lie Manifolds
The problem of determining the domain of the closure of the Laplace-Beltrami operator on a 2D almost-Riemannian manifold is considered. Using tools...
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Natural Differential Invariants and Equivalence of Third Order Nonlinear Differential Operators
AbstractWe give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of the third...
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On the Algebra of Operators Corresponding to the Union of Smooth Submanifolds
For a pair of smooth transversally intersecting submanifolds in some envelo** smooth manifold, we study the algebra generated by pseudodifferential...
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Pseudo-Differential Operators of Homogeneous Symbol Class Associated with the Weinstein Transform
In this paper, pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced. The boundedness...
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Casimir preserving stochastic Lie–Poisson integrators
Casimir preserving integrators for stochastic Lie–Poisson equations with Stratonovich noise are developed, extending Runge–Kutta Munthe-Kaas methods....
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SYMPLECTIC DIRAC OPERATORS FOR LIE ALGEBRAS AND GRADED HECKE ALGEBRAS
The aim of this paper is to define a pair of symplectic Dirac operators ( D + , D – ) in an algebraic setting motivated by the analogy with the algebraic...
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CUBIC DIRAC OPERATORS AND THE STRANGE FREUDENTHAL–DE VRIES FORMULA FOR COLOUR LIE ALGEBRAS
The aim of this paper is to define cubic Dirac operators for colour Lie algebras. We give a necessary and sufficient condition to construct a colour...
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Discrete Pseudo-differential Operators and Applications to Numerical Schemes
We consider a class of discrete operators introduced by O. Chodosh, acting on infinite sequences and mimicking standard properties of...
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Differential Graded Lie Algebras
In this chapter we introduce the basic algebraic theory of differential graded vector spaces and differential graded Lie algebras over an arbitrary...
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On the Dual Representation of the Congruence Kernels and the Related Delsarte Type Transmutations of Multidimensional Differential Operators
We analyze a dual representation of the congruence operator kernels subject to a pair of multidimensional differential operators on a Hilbert space...