Yury Popov

activity

20182021

collaborators

5 papers

math.RA2021

The geometric classification of $2$ -step nilpotent algebras and applications

Mikhail Ignatyev, Ivan Kaygorodov, Yury Popov

We give a geometric classification of complex $n$ -dimensional $2$ -step nilpotent (all, commutative and anticommutative) algebras. Namely, has been found the number of irreducible c…

math.RA2019

Degenerations of nilpotent associative commutative algebras

Ivan Kaygorodov, Samuel A. Lopes, Yury Popov

We give a complete description of degenerations of complex $5$ -dimensional nilpotent associative commutative algebras.

math.RA2018

The universal conservative superalgebra

Ivan Kaygorodov, Yury Popov, Alexandr Pozhidaev

We introduce the class of conservative superalgebras, in particular, the superalgebra $U (V)$ of bilinear operations on a superspace $V .$ Moreover, we show that each conse…

math.RA2018

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 $\geq 3$ we show that any finite-dimen…

math.RA2018

Split Regular $H o m$ -Leibniz Color $3$ -Algebras

Ivan Kaygorodov, Yury Popov

We introduce and describe the class of split regular $H o m$ -Leibniz color $3$ -algebras as the natural extension of the class of split Lie algebras, split Leibniz algebras, split Lie…

The geometric classification of 2-step nilpotent algebras and applications

Degenerations of nilpotent associative commutative algebras

The universal conservative superalgebra

Representations of simple noncommutative Jordan superalgebras I

Split Regular Hom-Leibniz Color 3-Algebras

The geometric classification of $2$ -step nilpotent algebras and applications

Split Regular $H o m$ -Leibniz Color $3$ -Algebras