相关论文: Complete classifications of two-dimensional genera…

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 give classification of two-dimensional real evolution algebras. For several chains of evolution algebras we study their classification dynamics.

The classification, up to isomorphism, of two-dimensional (not necessarily commutative) Jordan algebras over algebraically closed fields and $\mathbb{R}$ is presented in terms of their matrices of structure constants.

We developed a new proper method for classifying $n$-dimensional derived Jordan algebras, and apply it to the classification of $3$-dimensional derived Jordan algebras. As a byproduct, we have the algebraic classification of $3$-dimensional…

We give the algebraic and geometric classification of complex four-dimensional Jordan superalgebras. In particular, we describe all irreducible components in the corresponding varieties.

Decomposition algebras and axial decomposition algebras are classes of commutative nonassociative algebras which are generalizations of axial algebras. The classes decomposition algebras, axial decomposition al;gebras and non-primitive…

This paper is devoted to the description of complex finite-dimensional algebras of level two. We obtain the classification of algebras of level two in the varieties of Jordan, Lie and associative algebras.

In this paper, we mainly study Jordan derivations of dual extension algebras and those of generalized one-point extension algebras. It is shown that every Jordan derivation of dual extension algebras is a derivation. As applications, we…

A complete classifications, up to isomorphism, of two-dimensional associative and diassociative algebras over any basic field are given.

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…

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 study finite-dimensional commutative algebras, which satisfy the Jacobi identity. Such algebras are Jordan algebras. We describe some of their properties and give a classification in dimensions $n<7$ over algebraically closed fields of…

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…

We classify, up to isomorphism and up to equivalence, involutions on graded-division finite-dimensional simple real (associative) algebras, when the grading group is abelian.

The automorphisms groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.

We describe degenerations of three-dimensional Jordan superalgebras over $\mathbb{C}$. In particular, we describe all irreducible components in the corresponding varieties.

The algebraic and geometric classifications of complex $3$-dimensional noncommutative Jordan superalgebras are given. In particular, we obtain the algebraic and geometric classification of $3$-dimensional Kokoris and standard superalgebras,…

A complete classification of two-dimensional algebras over algebraically closed fields is provided

In this paper we classify a family of three-dimensional real evolution algebras. We also consider an evolution operator for an evolution algebra and find fixed points of this operator for two and three-dimensional cases. Then we construct…

Models of all the gradings on the exceptional simple Lie algebras induced by Jordan subgroups of their groups of automorphisms are provided.