73 citations · 1.5k across the 132 of their papers we have counts for
11 papers · 1 filter
The structure of simple noncommutative Jordan superalgebras
Ivan Kaygorodov, Artem Lopatin, Yury Popov
In this paper we describe all subalgebras and automorphisms of simple noncommutative Jordan superalgebras and and compute the derivations of the nontrivia…
Separating invariants for 2x2 matrices
Ivan Kaygorodov, Artem Lopatin, Yury Popov
A minimal separating set is found for the algebra of matrix invariants of several 2x2 matrices over an infinite field of arbitrary characteristic
Complete classification of algebras of level two
Ivan Kaygorodov, Yury Volkov
The main result of the paper is the classification of all (nonassociative) algebras of level two, i.e. such algebras that maximal chains of nontrivial degenerations starting at the…
On a ternary generalization of Jordan algebras
Ivan Kaygorodov, Alexander Pozhidaev, Paulo Saraiva
Based on the relation between the notions of Lie triple systems and Jordan algebras, we introduce the -ary Jordan algebras,an -ary generalization of Jordan algebras obtained…
Degenerations of Jordan Superalgebras
María Alejandra Alvarez, Isabel Hernández, Ivan Kaygorodov
We describe degenerations of three-dimensional Jordan superalgebras over . In particular, we describe all irreducible components in the corresponding varieties.
Abelian groups gradings on null-filiform and one-parametric filiform Leibniz algebras
Antonio Calderón, Luisa Camacho, Ivan Kaygorodov +1
We classify, up to equivalences, all abelian groups gradings on null-filiform and one-parametric filiform Leibniz algebras. Any grading on a null-filiform Leibniz algebra is toral…
-Modules over linear spaces by -linear maps admitting a multiplicative basis
Elisabete Barreiro, Ivan Kaygorodov, José M. Sánchez
We study the structure of certain -modules over linear spaces with restrictions neither on the dimensions of and nor on the b…
On Thompson's conjecture for finite simple exceptional groups of Lie type
Ilya Gorshkov, Ivan Kaygorodov, Andrei Kukharev +1
Let be a finite group, be the set of conjugacy classes of the group . In the present paper it is proved if , where is a finite group with t…
Degenerations of Jordan Algebras and ''Marginal'' Algebras
Ilya Gorshkov, Ivan Kaygorodov, Yury Popov
We describe all degenerations of the variety of Jordan algebras of dimension three over In particular, we describe all irreducible components in $…
The geometric classification of Leibniz algebras
Nurlan Ismailov, Ivan Kaygorodov, Yury Volkov
We describe all rigid algebras and all irreducible components in the variety of four dimensional Leibniz algebras over In particular, we prove tha…
The variety of -dimensional algebras over an algebraically closed field
Ivan Kaygorodov, Yury Volkov
The work is devoted to the variety of -dimensional algebras over an algebraically closed field. Firstly, we classify such algebras modulo isomorphism. Then we describe the degen…