73 citations · 1.5k across the 132 of their papers we have counts for
141 papers
Degenerations of Jordan algebras
Victor Bovdi, Ivan Kaygorodov, Yury Popov +2
We describe all degenerations of complex -dimensional Jordan algebras and of complex -dimensional nilpotent Jordan algebras. The proofs do not use other papers on degeneratio…
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=\{…
Evolution algebras: a survey of results and a list of open problems
Ivan Kaygorodov, Cándido Mart\'ın González, Antonio Viruel
Evolution algebras, introduced by J. P. Tian as an algebraic model of non- Mendelian inheritance, are commutative algebras with a basis whose distinct elements multiply to zero. Th…
Classification of -dimensional unital commutative algebras
Maqpal Eraliyeva, Ivan Kaygorodov
We present the complete classification of non-isomorphic complex -dimensional unital commutative algebras. Every such algebra decomposes canonically as , w…
A unified approach to the definition of anti-algebras
Ivan Kaygorodov, Abror Khudoyberdiyev, Bauyrzhan Sartayev
We introduce the arseille anti-construction for varieties of algebras defined by multilinear identities of degree , obtained by changing the sign of…
The geometric classification of Novikov-Poisson and Gelfand-Dorfman algebras
Zeyu Hao, Ivan Kaygorodov, Azamat Saydaliyev +1
We give the geometric classification of complex 3-dimensional Novikov-Poisson and Gelfand-Dorfman algebras. In particular, we prove that the variety of complex 3-dimensional Noviko…
Quasi-derivations of Block Lie algebras
Ivan Kaygorodov, Abror Khudoyberdiyev, Zarina Shermatova
We compute quasi-derivations of Block Lie algebras . In particular, we prove that has various nontrivial quasi-derivations, i.e., quasi-derivations…
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…
Integro-derivation Dzhumadildaev algebras: from the algebra of polynomials
Ivan Kaygorodov, Naurizbay Uzakbaev
This paper introduces and investigates some properties of algebras constructed from the algebra of polynomials via derivation and integration operators using a process presented by…
Unital -dimensional structurable algebras: classification, properties and -construction
Kobiljon Abdurasulov, Maqpal Eraliyeva, Ivan Kaygorodov
This paper is devoted to the classification and studying properties of complex unital -dimensional structurable algebras. We provide a complete list of non-isomorphic classes, i…
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…
-Leibniz algebras and related -type algebras
Jobir Adashev, Ivan Kaygorodov
This paper introduces and investigates the structure of -Leibniz algebras, which serve as a parametric generalization of classical Leibniz algebras defined by a scalar . The…
Quasi-derivations of Witt and related algebras
Ivan Kaygorodov, Abror Khudoyberdiyev, Zarina Shermatova
In the present work, we compute quasi-derivations of the Witt algebra and some algebras well-related to the Witt algebra. Namely, we prove that each quasi-derivation of the Witt al…
The complete classification of irreducible components of varieties of Jordan superalgebras
Renato Fehlberg Júnior, Ivan Kaygorodov, Azamat Saydaliyev
The aim of the present short note is to answer the open questions posted by Hernández, Martin, and Rodrigues in {\rm \cite{p1,p2}}. The obtained results give the complete classific…
-Novikov and -Novikov--Poisson algebras
Ivan Kaygorodov
This article considers the structure and properties of -Novikov algebras, a generalization of Novikov algebras characterized by a scalar parameter . Unlike Novikov algebras,…
Nonassociative algebras of anti-biderivation-type
Saïd Benayadi, Said Boulmane, Ivan Kaygorodov
The main purpose of this paper is to study the class of Jacobi-Jordan-admissible algebras whose product is an anti-biderivation of the related Jacobi-Jordan algebra; we call them $…
Polynomial invariants for 3-dimensional Leibniz algebras
Ivan Kaygorodov, Artem Lopatin
For each 3-dimensional non-Lie Leibniz algebra over the complex numbers, we describe the algebra of polynomial invariants and determine its group of automorphisms. As a consequence…
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…
The geometric classification of non-associative algebras: a survey
Ivan Kaygorodov, Mykola Khrypchenko, Pilar Páez-Guillán
This is a survey on the geometric classification of different varieties of algebras (nilpotent, nil-, associative, commutative associative, cyclic associative, Jordan, Kokoris, sta…