Related papers: Finitely generated algebras with involution and th…
We consider associative algebras with involution graded by a finite abelian group G over a field of characteristic zero. Suppose that the involution is compatible with the grading. We represent conditions permitting PI-representability of…
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…
We consider associative algebras with involution over a field of characteristic zero. We proved that any algebra with involution satisfies the same identities with involution as the Grassmann envelope of some finite dimensional $Z_4$-graded…
In this short note, we describe the so-called homogeneous involution on finite-dimensional graded-division algebra over an algebraically closed field. We also compute their graded polynomial identities with involution. As pointed out by L.…
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…
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…
In this paper we show that evolution algebras over any given field $\Bbbk$ are universally finite. In other words, given any finite group $G$, there exist infinitely many regular evolution algebras $X$ such that $Aut(X)\cong G$. The proof…
The nilpotency degree of a relatively free finitely generated associative algebra with the identity $x^n=0$ is studied over finite fields.
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…
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…
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…
Given an evolution algebra associated to a connected finite graph $\Gamma$, we exhibit a free action of the group of symmetries of $\Gamma$ on the set of automorphisms of the algebra. This allows us to explicitly describe this set and we…
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 paper we describe graded automorphisms and antiautomorphisms of finite order on matrix algebras endowed with a group gradings by a finite abelian group over an arbitrary algebraically closed field of charcteristic different from 2.
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…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
Genetic and evolution algebras arise naturally from applied probability and stochastic processes. Gibbs measures describe interacting systems commonly studied in thermodynamics and statistical mechanics with applications in several fields.…
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 give a complete description of the varieties of associative algebras over a field of characteristic zero which satisfy a polynomial identity of third degree.
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…