55 citations · 270 across the 16 of their papers we have counts for
18 papers
Degenerations of Jordan algebras
Victor Bovdi, Ivan Kaygorodov, Yury Popov +2
We describe all degenerations of complex -dimensional Jordan algebras and of complex -dimensional nilpotent Jordan algebras. The proofs do not use other papers on degeneratio…
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 algebraic and geometric classification of nilpotent terminal algebras
Ivan Kaygorodov, Mykola Khrypchenko, Yury Popov
We give algebraic and geometric classifications of -dimensional complex nilpotent terminal algebras. Specifically, we find that, up to isomorphism, there are one-parameter…
Degenerations of nilpotent associative commutative algebras
Ivan Kaygorodov, Samuel A. Lopes, Yury Popov
We give a complete description of degenerations of complex -dimensional nilpotent associative commutative algebras.
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…
Representations of simple noncommutative Jordan superalgebras I
Yury Popov
In this article we begin the study of representations of simple finite-dimensional noncommutative Jordan superalgebras. In the case of degree we show that any finite-dimen…
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…
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
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 $…
Degenerations of Zinbiel and nilpotent Leibniz algebras
Ivan Kaygorodov, Yury Popov, Alexandre Pozhidaev +1
We describe degenerations of four-dimensional Zinbiel and four-dimensional nilpotent Leibniz algebras over C. In particular, we describe all irreducible components in the correspon…
Generalized derivations of multiplicative -ary Hom- color algebras
Patricia Damas Beites, Ivan Kaygorodov, Yury Popov
We generalize the results of Leger and Luks, Zhang R. and Zhang Y.; Chen, Ma, Ni, Niu, Zhou and Fan; Kaygorodov and Popov about generalized derivations of color -ary algebras to…
Degenerations of binary Lie and nilpotent Malcev algebras
Ivan Kaygorodov, Yury Popov, Yury Volkov
We describe degenerations of four-dimensional binary Lie algebras, and five- and six-dimensional nilpotent Malcev algebras over \mathbb{C}. In particular, we describe all irreducib…
Jordan algebras admitting derivations with invertible values
Ivan Kaygorodov, Artem Lopatin, Yury Popov
The notion of derivation with invertible values as a derivation of ring with unity that only takes multiplicatively invertible or zero values appeared in a paper of Bergen, Herstei…
Generalized derivations of (color) n-ary algebras
Ivan Kaygorodov, Yury Popov
We generalize the results of Leger and Luks about generalized derivations of Lie algebras to the case of color -ary -algebras. Particularly, we prove some properties of gener…
A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations
Ivan Kaygorodov, Yury Popov
Moens proved that a finite-dimensional Lie algebra over field of characteristic zero is nilpotent if and only if it has an invertible Leibniz-derivation. In this article we prove t…
Conservative algebras of 2-dimensional algebras
Ivan Kaygorodov, Artem Lopatin, Yury Popov
We describe derivations and subalgebras of codimensions 1 of conservative algebras of small dimensions.
Identities of sum of two PI-algebras in the case of positive characteristic
Ivan Kaygorodov, Artem Lopatin, Yury Popov
We consider the following question posted by K.I. Beidar and A.V. Mikhalev in 1995 for an associative ring : is it true that if the subrings and satisfy poly…