41 citations · 93 across the 8 of their papers we have counts for
9 papers · 1 filter
Commutative algebras are ideals of evolution algebras
Cristina Costoya, Amir Fernández Ouaridi, Antonio Viruel
We prove that every finite-dimensional commutative algebra can be embedded as an ideal of a finite-dimensional evolution algebra. We then determine the smallest possible dimension…
On simple transposed Poisson algebras
Amir Fernández Ouaridi
We develop a structure theory for transposed Poisson algebras over fields of characteristic different from two. In particular, we prove that every finite-dimensional transposed Poi…
Abelian Subalgebras and Ideals of Maximal Dimension in Poisson algebras
Amir Fernández Ouaridi, Rosa María Navarro, David A. Towers
This paper studies the abelian subalgebras and ideals of maximal dimension of Poisson algebras of dimension . We introduce the invariants and for Poisson a…
The algebraic and geometric classification of transposed Poisson algebras
Patrícia Damas Beites, Amir Fernández Ouaridi, Ivan Kaygorodov
The algebraic and geometric classification of all complex -dimensional transposed Poisson algebras is obtained. Also, we discuss strong special -dimensional transposed Poisso…
Zinbiel superalgebras
Luisa María Camacho, Amir Fernández Ouaridi, Ivan Kaygorodov +1
Throughout the current paper, we extend the study of Zinbiel algebras to Zinbiel superalgebras. In particular, we show that all the Zinbiel superalgebras over an arbitrary field ar…
Non-degenerate evolution algebras
Antonio Jesús Calderón Martín, Amir Fernández Ouaridi, Ivan Kaygorodov
In this paper we introduce a new invariant for a non-degenerate evolution algebra, which consists of an ordered sequence of evolution algebras of lower dimension, belonging all of…
Conservative algebras of -dimensional algebras, IV
Amir Fernández Ouaridi, Ivan Kaygorodov, Cándido Martín González
The notion of conservative algebras appeared in a paper by Kantor in 1972. Later, he defined the conservative algebra of all algebras (i.e. bilinear maps) on the -dimensi…
Degenerations of nilpotent algebras
Amir Fernández Ouaridi, Ivan Kaygorodov, Mykola Khrypchenko +1
We give a complete description of degenerations of -dimensional nilpotent algebras, -dimensional nilpotent commutative algebras and -dimensional nilpotent anticommutative…
Classification of bilinear maps with radical of codimension 2
Antonio Jesús Calderón, Amir Fernández Ouaridi, Ivan Kaygorodov
Let be an -dimensional linear space over an algebraically closed base field. We provide a classification, up to equivalence, of all of the bilinear maps $f:{\mathb…