73 citations · 1.5k across the 132 of their papers we have counts for
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The algebraic classification of nilpotent algebras
Ivan Kaygorodov, Mykola Khrypchenko, Samuel A. Lopes
We give the complete algebraic classification of all complex 4-dimensional nilpotent algebras. The final list has 234 (parametric families of) isomorphism classes of algebras, 66 o…
Poisson Structures on Finitary Incidence Algebras
Ivan Kaygorodov, Mykola Khrypchenko
We give a full description of the Poisson structures on the finitary incidence algebra of an arbitrary poset over a commutative unital ring .
-derivations of Lie algebras and transposed Poisson algebras
Bruno Leonardo Macedo Ferreira, Ivan Kaygorodov, Viktor Lopatkin
A relation between -derivations of Lie algebras and transposed Poisson algebras was established. Some non-trivial transposed Poisson algebras with a certain Lie algebr…
Central extensions of filiform Zinbiel algebras
Luisa M. Camacho, Iqboljon Karimjanov, Ivan Kaygorodov +1
In this paper we describe central extensions (up to isomorphism) of all complex null-filiform and filiform Zinbiel algebras. It is proven that every non-split central extension of…
One-generated nilpotent terminal algebras
Ivan Kaygorodov, Abror Khudoyberdiyev, Aloberdi Sattarov
We give an algebraic classification of complex -dimensional one-generated nilpotent terminal algebras.
The geometric classification of nilpotent -algebras
Ivan Kaygorodov, Mykola Khrypchenko
We give a geometric classification of complex -dimensional nilpotent -algebras. The corresponding geometric variety has dimension 18 and decomposes into irred…
The algebraic classification of nilpotent -algebras
Ivan Kaygorodov, Mykola Khrypchenko
We give an algebraic classification of complex -dimensional nilpotent -algebras.
Commuting maps on alternative rings
Bruno Leonardo Macedo Ferreira, Ivan Kaygorodov
Suppose is a ,-torsion free unital alternative ring having an idempotent element which satisfies $x \mathfrak{R} \cdot e_i = \…
One-generated nilpotent Novikov algebras
Luisa M. Camacho, Iqboljon Karimjanov, Ivan Kaygorodov +1
We give a classification of 5- and 6-dimensional complex one-generated nilpotent Novikov algebras
Lie maps on alternative rings preserving idempotents
Bruno Leonardo Macedo Ferreira, Henrique Guzzo, Ivan Kaygorodov
Let and unital ,-torsion free alternative rings and be a surjective Lie multiplicative map that preserves idempotents. Assume that $\Re…
Non-associative central extensions of null-filiform associative algebras
Ivan Kaygorodov, Samuel A. Lopes, Pilar Páez-Guillán
We give the algebraic classification of alternative, left alternative, Jordan, bicommutative, left commutative, assosymmetric, Novikov and left symmetric central extensions of null…
The algebraic and geometric classification of nilpotent anticommutative algebras
Ivan Kaygorodov, Mykola Khrypchenko, Samuel A. Lopes
We give algebraic and geometric classifications of -dimensional complex nilpotent anticommutative algebras. Specifically, we find that, up to isomorphism, there are one-par…