73 citations · 1.5k across the 132 of their papers we have counts for
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The algebraic and geometric classification of nilpotent Novikov algebras
Iqboljon Karimjanov, Ivan Kaygorodov, Abror Khudoyberdiyev
This paper is devoted to give the complete algebraic and geometric classification of -dimensional nilpotent Novikov algebras over
The universal conservative superalgebra
Ivan Kaygorodov, Yury Popov, Alexandr Pozhidaev
We introduce the class of conservative superalgebras, in particular, the superalgebra of bilinear operations on a superspace Moreover, we show that each conse…
The classification of -dimensional rigid algebras
Antonio Jesús Calderón, Amir Fernández Ouaridi, Ivan Kaygorodov
Using the algebraic classification of all -dimensional algebras, we give the algebraic classification of all -dimensional rigid, conservative and terminal algebras over an al…
Central extensions of filiform associative algebras
Iqboljon Karimjanov, Ivan Kaygorodov, Manuel Ladra
In this paper we describe central extensions (up to isomorphism) of all complex null-filiform and filiform associative algebras.
Degenerations of Leibniz and anticommutative algebras
Nurlan Ismailov, Ivan Kaygorodov, Yury Volkov
We describe all degenerations of three dimensional anticommutative algebras and of three dimensional Leibniz algebras over In…
Split Regular -Leibniz Color -Algebras
Ivan Kaygorodov, Yury Popov
We introduce and describe the class of split regular -Leibniz color -algebras as the natural extension of the class of split Lie algebras, split Leibniz algebras, split Lie…
Classification of bilinear maps with radical of codimension 2
Antonio Jesús Calderón, Amir Fernández Ouaridi, Ivan Kaygorodov
Let be an -dimensional linear space over an algebraically closed base field. We provide a classification, up to equivalence, of all of the bilinear maps $f:{\mathb…
Rota-type operators on null-filiform associative algebras
I. A. Karimjanov, Ivan Kaygorodov, Manuel Ladra
We give the description of homogeneous Rota-Baxter operators, Reynolds operators, Nijenhuis operators, Average operators and differential operator of weight 1 of null-filiform asso…
Higher Derivations of Finitary Incidence Algebras
Ivan Kaygorodov, Mykola Khrypchenko, Feng Wei
Let be a partially ordered set, a commutative unital ring and the finitary incidence algebra of over . We prove that each -linear higher derivation of $…
The classification of -dimensional anticommutative algebras with -dimensional annihilator
Antonio Jesús Calderón, Amir Fernández Ouaridi, Ivan Kaygorodov
We give the classification of all -dimensional anticommutative complex algebras with -dimensional annihilator. Namely, we describe all central extensions of all -dimen…
Decompositions of linear spaces induced by -linear maps
Antonio Jesús Calderón, Ivan Kaygorodov, Paulo Saraiva
Let be an arbitrary linear space and an -linear map. It is proved that, for each choice of a basis ${\math…
-Ary generalized Lie-type color algebras admitting a quasi-multiplicative basis
Elisabete Barreiro, Antonio Jesús Calderón, Ivan Kaygorodov +1
The class of generalized Lie-type color algebras contains the ones of generalized Lie-type algebras, of -Lie algebras and superalgebras, commutative Leibniz -ary algebras and…