73 citations · 1.5k across the 132 of their papers we have counts for
12 papers · 1 filter
One-generated nilpotent bicommutative algebras
Ivan Kaygorodov, Pilar Páez-Guillán, Vasily Voronin
We give a classification of - and -dimensional complex one-generated nilpotent bicommutative algebras.
The algebraic classification of nilpotent commutative algebras
Doston Jumaniyozov, Ivan Kaygorodov, Abror Khudoyberdiyev
This paper is devoted to the complete algebraic classification of complex -dimensional nilpotent commutative algebras. Our method of classification is based on the standard meth…
The geometric classification of nilpotent commutative -algebras
Doston Jumaniyozov, Ivan Kaygorodov, Abror Khudoyberdiyev
We give a geometric classification of complex -dimensional nilpotent commutative -algebras. The corresponding geometric variety has dimension and decomposes…
The algebraic classification of nilpotent commutative -algebras
Doston Jumaniyozov, Ivan Kaygorodov, Abror Khudoyberdiyev
An algebraic classification of complex -dimensional nilpotent commutative -algebras is given. This classification is based on an algebraic classification of compl…
Local and -local derivations of simple -ary algebras
Bruno Leonardo Macedo Ferreira, Ivan Kaygorodov, Karimbergen Kudaybergenov
In the present paper, we prove that every local and -local derivation of the complex finite-dimensional simple Filippov algebra is a derivation. As a corollary we have the descr…
The algebraic and geometric classification of nilpotent right alternative algebras
Nurlan Ismailov, Ivan Kaygorodov, Manat Mustafa
We present algebraic and geometric classifications of the -dimensional complex nilpotent right alternative algebras. Specifically, we find that, up to isomorphism, there are onl…
The algebraic and geometric classification of nilpotent left-symmetric algebras
Jobir Adashev, Ivan Kaygorodov, Abror Khudoyberdiyev +1
This paper is devoted to the complete algebraic and geometric classification of complex -dimensional nilpotent left-symmetric algebras. The corresponding geometric variety has d…
On anticommutative algebras for which is a derivation
Ivan Kaygorodov, Pasha Zusmanovich
We study anticommutative algebras with the property that commutator of any two multiplications is a derivation.
Central extensions of 3-dimensional Zinbiel algebras
María Alejandra Alvarez, Thiago Castilho de Mello, Ivan Kaygorodov
We describe all central extensions of all -dimensional non-zero complex Zinbiel algebras. As a corollary, we have a full classification of -dimensional non-trivial complex Zi…
The geometric classification of -step nilpotent algebras and applications
Mikhail Ignatyev, Ivan Kaygorodov, Yury Popov
We give a geometric classification of complex -dimensional -step nilpotent (all, commutative and anticommutative) algebras. Namely, has been found the number of irreducible c…
The geometric classification of nilpotent algebras
Ivan Kaygorodov, Mykola Khrypchenko, Samuel A. Lopes
We give a geometric classification of -dimensional nilpotent, commutative nilpotent and anticommutative nilpotent algebras. We prove that the corresponding geometric varieties a…
One-generated nilpotent assosymmetric algebras
Ivan Kaygorodov, Farukh Mashurov
We give the classification of - and -dimensional complex one-generated nilpotent assosymmetric algebras.