Related papers: Isomorphism Classes of Idempotent Evolution Algebr…
We study the automorphism group of an idempotent evolution algebra, show that any finite group can be the automorphism group of an evolution algebra, and describe certain evolution algebras with given automorphism groups. In particular, we…
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…
We classify all finite-dimensional connected Hopf algebras with large abelian primitive spaces. We show that they are Hopf algebra extensions of restricted enveloping algebras of certain restricted Lie algebras. For any abelian matched pair…
Let $\mathcal{E}$ be the class of finite-dimensional algebras isomorphic to endomorphism algebras of silting complexes over hereditary abelian categories. It is proved that the class $\mathcal{E}$ is closed under taking idempotent…
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 study the class of all algebras that are isotopic to a Hurwitz algebra. Isomorphism classes of such algebras are shown to correspond to orbits of a certain group action. A complete, geometrically intuitive description of the category of…
We classify conjugacy classes of involutions in the isometry groups of nondegenerate, symmetric bilinear forms over the field of two elements. The new component of this work focuses on the case of an orthogonal form on an even dimensional…
In this paper we classify the isomorphism classes of four dimensional nilpotent associative algebras over a field F, studying regular subgroups of the affine group AGL_4(F). In particular we provide explicit representatives for such classes…
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…
Let $R$ be a semilocal principal ideal domain. Two algebraic objects over $R$ in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all…
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 give a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. We also discuss various generalizations of this problem and some…
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…
We show that a class of algebras is closed under the taking of homomorphic images and direct products if and only if the class consists of all algebras that satisfy a set of (generally simultaneous) equations. For classes of regular…
Automorphisms of order $2$ are studied in order to understand generalized symmetric spaces. The groups of type $E_6$ we consider here can be realized as both the group of linear maps that leave a certain determinant invariant, and also as…
We prove that the isomorphism problem for group algebras reduces to group algebras over finite extensions of the prime field. In particular, the modular isomorphism problem reduces to finite modular group algebras.
Isomorphy classes of k-involutions have been studied for their correspondence with generalized symmetric spaces of algebraic groups. This is a continuation of papers written by A.G. Helminck and collaborators that are regarding algebraic…
The type and several invariant subspaces related to the upper annihilating series of finite-dimensional nilpotent evolution algebras are introduced. These invariants can be easily computed from any natural basis. Some families of nilpotent…
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 =…