57 citations · 144 across the 19 of their papers we have counts for
21 papers
Simple finite-dimensional binary Lie superalgebras
Hani Abdelwahab, Ivan Kaygorodov
We prove that every complex finite-dimensional simple binary Lie superalgebra with non-zero odd part is either a simple Lie superalgebra, and hence is one of the superalgebras of K…
The algebraic and geometric classification of -Poisson algebras
Hani Abdelwahab, Kobiljon Abdurasulov, Ivan Kaygorodov
-Poisson (ternary Nambu--Poisson) algebras are the algebras of observables of Nambu mechanics, the generalization of Hamiltonian mechanics in which the time evolution $\dot f=\{…
The algebraic and geometric classification of -Novikov algebras
Hani Abdelwahab, Ivan Kaygorodov, Roman Lubkov
The notion of -Novikov algebras was introduced recently as a generalization of Novikov and bicommutative algebras. It looks like -Novikov algebras have a richer structure tha…
The algebraic and geometric classification of noncommutative Jordan superalgebras
Hani Abdelwahab, Ivan Kaygorodov, Abror Khudoyberdiyev
The algebraic and geometric classifications of complex -dimensional noncommutative Jordan superalgebras are given. In particular, we obtain the algebraic and geometric classific…
The algebraic and geometric classification of commutative post-Lie algebras
Hani Abdelwahab, Kobiljon Abdurasulov, Ivan Kaygorodov
We study commutative post-Lie algebras {\rm CPA}s from an algebraic point of view. Firstly, we find some new identities in {\rm CPA}, which shows that the commutative multipl…
The algebraic and geometric classification of right alternative superalgebras
Hani Abdelwahab, Ivan Kaygorodov, Abror Khudoyberdiyev
The algebraic and geometric classifications of complex -dimensional right alternative superalgebras are given. As a byproduct, we have the algebraic and geometric classification…
The algebraic and geometric classification of derived Jordan and bicommutative algebras
Hani Abdelwahab, Ivan Kaygorodov, Roman Lubkov
We developed a new proper method for classifying -dimensional derived Jordan algebras, and apply it to the classification of -dimensional derived Jordan algebras. As a byprod…
The algebraic and geometric classification of right alternative and semi-alternative algebras
Hani Abdelwahab, Ivan Kaygorodov, Roman Lubkov
The algebraic and geometric classifications of complex -dimensional right alternative and semi-alternative algebras are given. As corollaries, we have the algebraic and geometri…
-Poisson and transposed -Poisson algebras
Hani Abdelwahab, Ivan Kaygorodov, Bauyrzhan Sartayev
We present a comprehensive study of two new Poisson-type algebras. Namely, we are working with -Poisson and transposed -Poisson algebras. Our research shows that these algebr…
Classification of -dimensional complex Poisson algebras
Hani Abdelwahab, José María Sánchez
The present paper is devoted to the complete classification of -dimensional complex Poisson algebras, taking into account a classification, up to isomorphism, of the complex com…
Shift associative algebras
Hani Abdelwahab, Ivan Kaygorodov, Bauyrzhan Sartayev
We present a comprehensive study of algebras satisfying the identity named as shift associative algebras. Our research shows that these algebras are related to many…
The algebraic and geometric classification of noncommutative Jordan algebras
Hani Abdelwahab, Kobiljon Abdurasulov, Ivan Kaygorodov
In this paper, we develop a method to obtain the algebraic classification of noncommutative Jordan algebras from the classification of Jordan algebras of the same dimension. We use…
The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras
Hani Abdelwahab, Ivan Kaygorodov, Abdenacer Makhlouf
In this paper, we develop a method to obtain the algebraic classification of compatible pre-Lie algebras from the classification of pre-Lie algebras of the same dimension. We use t…
Degenerations of Poisson-type algebras
Hani Abdelwahab, Amir Fernández Ouaridi, Ivan Kaygorodov
The degenerations of Poisson-type algebras are studied in the following varieties in dimension two: Leibniz--Poisson algebras, transposed Leibniz--Poisson algebras, Novikov--Poisso…
Decompositions of linear operators on pre-euclidean spaces by means of graphs
Hani Abdelwahab, Elisabete Barreiro, Antonio J. Calderón +1
In this work we study a linear operator on a pre-euclidean space by using properties of a corresponding graph. Given a basis $\B$ of , we present a d…
Degenerations of Poisson algebras
Hani Abdelwahab, Amir Fernández Ouaridi, Cándido Martín González
We construct a method to obtain the algebraic classification of Poisson algebras defined on a commutative associative algebra, and we apply it to obtain the classification of the $…
The algebraic and geometric classification of nilpotent Lie triple systems up to dimension four
Hani Abdelwahab, Elisabete Barreiro, Antonio J. Calderón +1
In this paper we generalize the Skjelbred Sund method, used to classify nilpotent Lie algebras, in order to classify triple systems with non zero annihilator. We develop this metho…
The algebraic and geometric classification of nilpotent binary Lie algebras
Hani Abdelwahab, Antonio Jesús Calderón, Ivan Kaygorodov
The paper is devoted to give the complete algebraic classification of nilpotent binary Lie algebras of dimension over an arbitrary base field of characteris…
Five-dimensional nilpotent evolution algebras
A. S. Hegazi, Hani Abdelwahab
The paper is devoted to give a complete classification of five-dimension nilpotent evolution algebras over an algebraically closed field. We obtained a list of 27 isolated non-isom…
Nilpotent evolution algebras over arbitrary fields
A. S. Hegazi, Hani Abdelwahab
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…
Classification of five-dimensional nilpotent Jordan algebras
A. S. Hegazi, Hani Abdelwahab
The paper is devoted to classify nilpotent Jordan algebras of dimension up to five over an algebraically closed field of characteristic not 2. We obtained a list of 35 isolated non…