73 citations · 1.5k across the 132 of their papers we have counts for
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The algebraic and geometric classification of antiassociative algebras
Renato Fehlberg Júnior, Ivan Kaygorodov, Crislaine Kuster
This paper is devoted to the complete algebraic and geometric classification of complex 4 and 5-dimensional antiassociative algebras. In particular, we proved that the variety of c…
The algebraic and geometric classification of transposed Poisson algebras
Patrícia Damas Beites, Amir Fernández Ouaridi, Ivan Kaygorodov
The algebraic and geometric classification of all complex -dimensional transposed Poisson algebras is obtained. Also, we discuss strong special -dimensional transposed Poisso…
Transposed Poisson structures on solvable and perfect Lie algebras
Ivan Kaygorodov, Abror Khudoyberdiyev
We described all transposed Poisson algebra structures on oscillator Lie algebras, i.e., on one-dimensional solvable extensions of the -dimensional Heisenberg algebra; on s…
Transposed Poisson structures on Lie incidence algebras
Ivan Kaygorodov, Mykola Khrypchenko
Let be a finite connected poset, a field of characteristic zero and the incidence algebra of over seen as a Lie algebra under the commutator product. In th…
The algebraic and geometric classification of nilpotent binary and mono Leibniz algebras
Kobiljon Abdurasulov, Ivan Kaygorodov, Abror Khudoyberdiyev
This paper is devoted to the complete algebraic and geometric classification of complex -dimensional nilpotent binary Leibniz and -dimensional nilpotent mono Leibniz algebras…
The algebraic and geometric classification of nilpotent Leibniz algebras
Kobiljon Abdurasulov, Ivan Kaygorodov, Abror Khudoyberdiyev
This paper is devoted to the complete algebraic and geometric classification of complex -dimensional nilpotent Leibniz algebras. In particular, the variety of complex -dimens…
Non-associative algebraic structures: classification and structure
Ivan Kaygorodov
These are detailed notes for a lecture on "Non-associative Algebraic Structures: Classification and Structure" which I presented as a part of my Agregação em Matemática e Applicaçõ…
Zinbiel superalgebras
Luisa María Camacho, Amir Fernández Ouaridi, Ivan Kaygorodov +1
Throughout the current paper, we extend the study of Zinbiel algebras to Zinbiel superalgebras. In particular, we show that all the Zinbiel superalgebras over an arbitrary field ar…
Transposed Poisson structures on the Lie algebra of upper triangular matrices
Ivan Kaygorodov, Mykola Khrypchenko
We describe transposed Poisson structures on the upper triangular matrix Lie algebra , , over a field of characteristic zero. We prove that, for , any such st…
Non-degenerate evolution algebras
Antonio Jesús Calderón Martín, Amir Fernández Ouaridi, Ivan Kaygorodov
In this paper we introduce a new invariant for a non-degenerate evolution algebra, which consists of an ordered sequence of evolution algebras of lower dimension, belonging all of…
Transposed Poisson structures on generalized Witt algebras and Block Lie algebras
Ivan Kaygorodov, Mykola Khrypchenko
We describe transposed Poisson structures on generalized Witt algebras and Block Lie algebras over a field of characteristic z…
Conservative algebras of -dimensional algebras, V
Ivan Kaygorodov, Dolores Martín Barquero, Cándido Martín González
The notion of conservative algebras appeared in a paper by Kantor in 1972. Later, he defined the conservative algebra of all algebras (i.e. bilinear maps) on the -dimensi…