Related papers: Centroid and algebraic properties of evolution alg…
We study evolution algebras of arbitrary dimension. We analyze in deep the notions of evolution subalgebras, ideals and non-degeneracy and describe the ideals generated by one element and characterize the simple evolution algebras. We also…
In this article, we introduce a relation including ideals of an evolution algebra and hereditary subsets of vertices of its associated graph and establish some properties among them. This relation allows us to determine maximal ideals and…
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…
We consider the intersection $\mathfrak{M}(A)$ of all maximal ideals of an evolution algebra $A$ and study the structure of the quotient $A/\M(A)$. In a previous work, maximal ideals have been related to hereditary subsets of a graph…
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…
Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution…
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…
The affine group scheme of automorphisms of an evolution algebra that is equal to its square, is shown to lie in an exact sequence, such that the other terms depend solely on the directed graph associated to the algebra. As a consequence,…
In this note we study associative dialgebras proving that the most interesting such structures arise precisely when the algebra is not semiprime. In fact the presence of some "perfection" property (simpleness, primitiveness, primeness or…
It is well-known that the space of derivations of $n$-dimensional evolution algebras with non-singular matrices is zero. On the other hand, the space of derivations of evolution algebras with matrices of rank $n-1$ has also been completely…
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…
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 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…
Let $k$ be an algebraically closed base field of characteristic zero. The category equivalence between central simple algebras and irreducible, generically free $PGL_n$-varieties is extended to the context of central simple algebras with…
The theory of path algebras is usually circunscripted to the study of representations, usually linked to finite graphs. In our work, we focus on studying the structure of path algebras over a field associated to arbitrary graphs. We…
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 study the space of derivations for some finite-dimensional evolution algebras, depending on the twin partition of an associated directed graph. For evolution algebras with a twin-free associated graph we prove that the space of…
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…
Leibniz algebras are non-antisymmetric generalizations of Lie algebras that have attracted substantial interest due to their close relation with the latter class. A Leibniz algebra $A$ is called perfect if it coincides with its derived…
In this paper we introduce the notion of evolution rank and give a decomposition of an evolution algebra into its annihilator plus extending evolution subspaces having evolution rank one. This decomposition can be used to prove that in…