Related papers: On Hilbert evolution algebras of a graph
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…
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.…
Evolution algebras are non-associative algebras. In this work we provide an extension of this class of algebras, in the context of Hilbert spaces, capable to deal with infinite-dimensional spaces. We illustrate the applicability of our…
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…
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…
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 article we study algebraic structures of function spaces defined by graphs and state spaces equipped with Gibbs measures by associating evolution algebras. We give a constructive description of associating evolution algebras to the…
A connected graph can be associated with two distinct evolution algebras. In the first case, the structural matrix is the adjacency matrix of the graph itself. In the second case, the structural matrix is the transition probabilities matrix…
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…
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…
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…
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…
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…
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…
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…
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…
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 the paper we give a complete classification of $2$-dimensional evolution algebras over algebraically closed fields, describe their groups of automorphisms and derivation algebras.
Evolution algebras are non-associative algebras that describe non-Mendelian hereditary processes and have connections with many other areas. In this paper we obtain necessary and sufficient conditions for a given algebra $A$ to be an…
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…