73 citations · 1.5k across the 132 of their papers we have counts for
16 papers · 1 filter
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…