Related papers: Classification of four dimensional perfect non-sim…
We classify three dimensional evolution algebras over a field having characteristic different from 2 and in which there are roots of orders 2, 3 and 7.
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.
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…
The paper is devoted to the study of annihilator extensions of evolution algebras and suggests an approach to classify finite-dimensional nilpotent evolution algebras. Subsequently nilpotent evolution algebras of dimension up to four are…
We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.
The starting point of this work is that the class of evolution algebras over a fixed field is closed under tensor product. This arises questions about the inheritance of properties from the tensor product to the factors and conversely. For…
We classify (possibly non commutative) algebras of low rank over a domain R. We first review results for algebras of rank 2 and for finite-dimensional division algebras over the real numbers. These results motivate us to consider which…
This work classifies three-dimensional simple evolution algebras over arbitrary fields. For this purpose, we use tools such as the associated directed graph, the moduli set, inductive limit group, Zariski topology and the dimension of the…
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…
We will study evolution algebras $A$ which are free modules of dimension $2$ over domains. Furthermore, we will assume that these algebras are perfect, that is $A^2=A$. We start by making some general considerations about algebras over…
In this paper we give classification of two-dimensional real evolution algebras. For several chains of evolution algebras we study their classification dynamics.
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…
In this paper we obtain the classification of $p$-nilpotent restricted Lie algebras of dimension at most four over a perfect field of characteristic p.
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…
The space of derivations of finite dimensional evolution algebras associated to graphs over a field with characteristic zero has been completely characterized in the literature. In this work we generalize that characterization by describing…
The paper is devoted to give a complete classification of five-dimension nilpotent evolution algebras over an algebraically closed field. We obtained a list of 27 isolated non-isomorphic nilpotent evolution algebras and 2 families of…
The paper presents a classification of quadratic extension algebras, also known as algebras of degree 2, as well as several characterizations of quaternion algebras over a field (of characteristic not 2). The presentation is not restricted…
In this work we investigate the derivations of $n-$dimensional complex evolution algebras, depending on the rank of the appropriate matrices. For evolution algebra with non-singular matrices we prove that the space of derivations is zero.…
A complete classifications of two-dimensional general, commutative, commutative Jordan, division and evolution real algebras are given. In the case of evolution algebras their groups of automorphisms and derivation algebras are described as…
We illustrate some simple ideas that can be used for obtaining a classification of small-dimensional solvable Lie algebras.Using these we obtain the classification of 3 and 4 dimensional solvable Lie algebras (over fields of any…