Related papers: Derivation of Five-Dimensional Lotka-Voltera Algeb…
We develop here a concept of deformed algebras through three examples and an application. Deformed algebras are obtained from a fixed algebra by deformation along a family of indexes, through formal series. We show how the example of…
The Volterra lattice is a well-known integrable family that is also a special class of replicator dynamics and whose members can be put in one-to-one correspondence with the directed cycle graphs. In this paper, we study a variation of the…
In this paper, we introduce the concept of inner derivations of low-dimensional Zinbiel algebras and investigate their properties. The primary objective of this study is to develop an algorithm to characterize the inner derivations of any…
Derivations extend the concept of differentiation from functions to algebraic structures as linear operators satisfying the Leibniz rule. In Lie algebras, derivations form a Lie algebra via the commutator bracket of linear endomorphisms.…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
We study multiple zeta values and their generalizations from the point of view of Rota--Baxter algebras. We obtain a general framework for this purpose and derive relations on multiple zeta values from relations in Rota--Baxter algebras.
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…
An approach to master symmetries of lattice equations is proposed by the use of discrete zero curvature equation. Its key is to generate non-isospectral flows from the discrete spectral problem associated with a given lattice equation. A…
The study of Hermitian forms on a real reductive group $G$ gives rise, in the unequal rank case, to a new class of Kazhdan-Lusztig-Vogan polynomials. These are associated with an outer automorphism $\delta$ of $G$, and are related to…
We consider 5D spaces which admit the most symmetric 3D subspaces. 5D vacuum Einstein equations are constructed and 5D analog of the mass function is found. The corresponding conservation law leads to 5D analog of Birkhoff's theorem. Hence…
The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and…
Nongraded infinite-dimensional Lie algebras appeared naturally in the theory of Hamiltonian operators, the theory of vertex algebras and their multi-variable analogues. They play important roles in mathematical physics. This survey article…
The concept of extended Hamiltonian systems allows the geometrical interpretation of several integrable and superintegrable systems with polynomial first integrals of degree depending on a rational parameter. Until now, the procedure of…
We obtain minimal dimension matrix representations for each indecomposable five-dimensional Lie algebra over $\R$ and justify in each case that they are minimal. In each case a matrix Lie group is given whose matrix Lie algebra provides the…
Inferring microbial community structure based on temporal metagenomics data is an important goal in microbiome studies. The deterministic generalized Lotka-Volterra differential (GLV) equations have been used to model the dynamics of…
This paper studies the restriction multiplicities of half-diagram modules for the partition algebra and their geometric interpretations. By specializing the Bowman-De Visscher-Orellana formula [BVC, Theorem 4.3] for restriction…
We investigate the structure and representation theory of finite-dimensional $\mathbb{Z}$-graded Lie algebras, including the corresponding root systems and Verma, irreducible, and Harish-Chandra modules. This extends the familiar theory for…
This work aims to bridge the gap between pure and applied research on scalar, linear Volterra equations by examining five major classes: integral and integro-differential equations with completely monotone kernels, such as linear…
In this part of the series five-dimensional tangent vectors are introduced first as equivalence classes of parametrized curves and then as differential-algebraic operators that act on scalar functions. I then examine their basic algebraic…
In the paper stochastic Volterra equations of nonscalar type in Hilbert space are studied. The aim of the paper is to provide some results on stochastic convolution and mild solutions to those Volterra equations. The motivation of the paper…