Related papers: Order Structures around Evolution Algebras
Information algebras arise from the idea that information comes in pieces which can be aggregated or combined into new pieces, that information refers to questions and that from any piece of information, the part relevant to a given…
Evolution algebras with one dimensional square are classified using the theory of inner product spaces. More precisely, for $A$ an evolution algebra with $\dim(A^2) = 1$ and $a$ a generator of $A^2$, the product of $A$ is given by $xy =…
Galaxies, in particular disc galaxies, contain a number of structures and substructures with well defined morphological, photometric and kinematic properties. Considerable theoretical effort has been put into explaining their formation and…
In various subjects including mathematics, one can hope to use mathematical thinking well when the right kinds of algebraic structure to consider can be discovered or spotted. Therefore, it would help to understand kinds of algebraic…
In this paper we introduce a new invariant for a non-degenerate evolution algebra, which consists of an ordered sequence of evolution algebras of lower dimension, belonging all of them to a specific family. We use this invariant to propose…
In the present paper we describe absolute nilpotent and some idempotent elements of an n- dimensional evolution algebra corresponding to two permutations and we decompose such algebras to the direct sum of evolution algebras corresponding…
We describe absolute nilpotent and some idempotent elements of an $n$- dimensional evolution algebra corresponding to two permutations and we decompose such algebras to the direct sum of evolution algebras corresponding to cycles of the…
The use of the properties of actions on an algebra to enrich the study of the algebra is well-trodden and still fashionable. Here, the notion and study of endomorphic elements of (Banach) algebras are introduced. This study is initiated, in…
We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Order and symmetry are main structural principles in mathematics. We give five examples where on the face of it order is not apparent, but deeper investigations reveal that they are governed by order structures. These examples are finite…
This paper is devoted to understanding the defining ideal of a Nichols algebra from the decomposition of specific elements in the group algebra of braid groups. A family of primitive elements are found and algorithms are proposed. To prove…
Evolution algebras are a new type of non-associative algebras which are inspired from biological phenomena. A special class of such algebras, called Markov evolution algebras, is strongly related to the theory of discrete time Markov…
Classification theory of elementary classes deals with first order (elementary) classes of structures (i.e. fixing a set T of first order sentences, we investigate the class of models of T with the elementary submodel notion). It tries to…
The paper is devoted to study new classes of chains of evolution algebras and their time-depending dynamics. Moreover, we construct some Rote-Baxter operators of such algebras.
First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…
By natural way the hierarchy structure is introduced on directed graphs with weighted adjacencies. Embedded system of algebras of subsets of the set of vertices of such digraph and it's consolidations, which vertices are the elementary sets…
Here we introduce researchers in algebraic biology to the exciting new field of cophylogenetics. Cophylogenetics is the study of concomitantly evolving organisms (or genes), such as host and parasite species. Thus the natural objects of…
In the paper we give a complete classification of $2$-dimensional evolution algebras over algebraically closed fields, describe their groups of automorphisms and derivation algebras.
Semifields are semirings in which every nonzero element has a multiplicative inverse. A rough classification uses the characteristic of the semifield, that is the isomorphism type of the semifield generated by the two neutral elements. For…