73 citations · 1.5k across the 132 of their papers we have counts for
14 papers · 1 filter
-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…
Mutations of algebras
Ivan Kaygorodov, Farukh Mashurov
We describe mutation elements in free algebras. Moreover, we construct a base of free mutation of free algebra. Using Cohn's criterion for the s…
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…
Degenerations of nilalgebras
Ivan Kaygorodov, Oleg Shashkov
All complex -dimensional nilalgebras were described. As a corollary, all degenerations in the variety of complex -dimensional nilalgebras were obtained.
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…
Transposed Poisson structures on Virasoro-type algebras
Ivan Kaygorodov, Abror Khudoyberdiyev, Zarina Shermatova
We compute -derivations on the deformed generalized Heisenberg-Virasoro algebras and on not-finitely graded Heisenberg-Virasoro algebras , $\widetild…
The algebraic classification of nilpotent bicommutative algebras
Kobiljon Abdurasulov, Ivan Kaygorodov, Abror Khudoyberdiyev
This paper is devoted to the complete algebraic classification of complex 5-dimensional nilpotent bicommutative algebras.
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 noncommutative Heisenberg algebras
Ivan Kaygorodov, Yury Volkov
We give the full description of all degenerations of complex five dimensional noncommutative Heisenberg algebras. As a corollary, we have the full description of all degenerations…
Transposed Poisson structures on Witt-type algebras
Ivan Kaygorodov, Abror Khudoyberdiyev, Zarina Shermatova
We compute -derivations on the deformative Schrödinger-Witt algebra, on not-finitely graded Witt algebras , and on not-finitely graded Heisenberg-Witt algebra…
Maps on the mirror Heisenberg-Virasoro algebra, II
Xuelian Guo, Ivan Kaygorodov, Liming Tang
This is the second paper in our series of papers dedicated to the study of maps on the mirror Heisenberg-Virasoro algebra. The first paper is dedicated to the study of unary maps a…
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…
The algebraic classification of nilpotent Novikov algebras
Kobiljon Abdurasulov, Ivan Kaygorodov, Abror Khudoyberdiyev
This paper is devoted to the complete algebraic classification of complex -dimensional nilpotent Novikov algebras.