Related papers: Volterra Evolution Algebras and Their Graphs
The present paper is devoted to genetic Volterra algebras. We first study characters of such algebras. We fully describe associative genetic Volterra algebras, in this case all derivations are trivial. In general setting, i.e. when the…
Evolution algebras are a special class of non-associative algebras exhibiting connections with different fields of Mathematics. Hilbert evolution algebras generalize the concept through a framework of Hilbert spaces. This allows to deal…
The structural constants of an evolution algebra is given by a quadratic matrix $A$. In this work we establish equivalence between nil, right nilpotent evolution algebras and evolution algebras, which are defined by upper triangular matrix…
The purpose of this paper is to study the structure of Lotka-Volterra algebras, the set of their idempotent elements and their group of automorphisms. These algebras are defined through antisymmetric matrices and they emerge in connection…
We study the basic relation between skew-symmetric Lotka-Volterra systems and graphs, both at the level of objects and morphisms, and derive a classification from it of skew-symmetric Lotka-Volterra systems in terms of graphs as well as in…
Hilbert evolution algebras generalize evolution algebras through a framework of Hilbert spaces. In this work we focus on infinite-dimensional Hilbert evolution algebras and their representation through a suitably defined weighted digraph.…
The paper is devoted to the study of finite dimensional complex evolution algebras. The class of evolution algebras isomorphic to evolution algebras with Jordan form matrices is described. For finite dimensional complex evolution algebras…
A digraph is attached to any evolution algebra. This graph leads to some new purely algebraic results on this class of algebras and allows for some new natural proofs of known results. Nilpotency of an evolution algebra will be proved to be…
In this work we study the space of derivations of non-degenerate evolution algebras. We improve some results obtained recently in the literature and, as a consequence, we advance in the description of the derivations for $n$-dimensional…
The theory of algebras with polynomial identities has developed significantly, with special attention devoted to the classification of varieties according to the asymptotic behavior of their codimension sequences. This sequence is a…
It is known that any multiplication of a finite dimensional algebra is determined by a matrix of structural constants. In general, this is a cubic matrix. Difficulty of investigation of an algebra depends on the cubic matrix. Such a cubic…
In this paper we study subalgebras of complex finite dimensional evolution algebras. We obtain the classification of nilpotent evolution algebras whose any subalgebra is an evolution subalgebra with a basis which can be extended to a…
In the paper a Volterra quadratic stochastic operators of three dimensional simplex into itself is considered.The full description of ergodic properties such operators is given.
The first part of the book is devoted to the symmetry approach to classification of scalar integrable evolution PDEs with two independent variables. In the second part systems of evolution equations with polynomial homogeneous right-hand…
Evolution algebras are non-associative algebras inspired from biological phenomena, with applications to or connections with different mathematical fields. There are two natural ways to define an evolution algebra associated to a given…
We consider an evolution algebra which corresponds to a bisexual population with a set of females partitioned into finitely many different types and the males having only one type. We study basic properties of the algebra. This algebra is…
In the present paper we study some algebraic properties of evolution algebras. Moreover, we reduce the study of evolution algebras of permutations to two special types of evolution algebras, idempotents and absolute nilpotent elements of…
In this article, we study the ergodicity of neutral retarded stochastic functional differential equations driven by $\alpha$-regular Volterra process. Based on the equivalence between neutral retarded stochastic functional differential…
We associate an square to any two dimensional evolution algebra. This geometric object is uniquely determined, does not depend on the basis and describes the structure and the behaviour of the algebra. We determine the identities of degrees…
In this paper, we introduce some particular families of graphicable algebras obtained by following a relatively new line of research, initiated previously by some of the authors. It consists of the use of certain objects of Discrete…