7 papers
Rota-Baxter operators and factorization of Lie affgebras
JiaJia Han, Abror Khudoyberdiyev, Yunzhou Xie +1
We introduce Rota-Baxter operators on Lie affgebras by an identity independent of the choice of origin and prove that they induce descendant Lie affgebra structures. We establish a…
A unified approach to the definition of anti-algebras
Ivan Kaygorodov, Abror Khudoyberdiyev, Bauyrzhan Sartayev
We introduce the arseille anti-construction for varieties of algebras defined by multilinear identities of degree , obtained by changing the sign of…
Quasi-derivations of Block Lie algebras
Ivan Kaygorodov, Abror Khudoyberdiyev, Zarina Shermatova
We compute quasi-derivations of Block Lie algebras . In particular, we prove that has various nontrivial quasi-derivations, i.e., quasi-derivations…
The algebraic and geometric classification of noncommutative Jordan superalgebras
Hani Abdelwahab, Ivan Kaygorodov, Abror Khudoyberdiyev
The algebraic and geometric classifications of complex -dimensional noncommutative Jordan superalgebras are given. In particular, we obtain the algebraic and geometric classific…
The algebraic and geometric classification of right alternative superalgebras
Hani Abdelwahab, Ivan Kaygorodov, Abror Khudoyberdiyev
The algebraic and geometric classifications of complex -dimensional right alternative superalgebras are given. As a byproduct, we have the algebraic and geometric classification…
Quasi-derivations of Witt and related algebras
Ivan Kaygorodov, Abror Khudoyberdiyev, Zarina Shermatova
In the present work, we compute quasi-derivations of the Witt algebra and some algebras well-related to the Witt algebra. Namely, we prove that each quasi-derivation of the Witt al…
Cohomological rigidity of conformal Galilei algebras and their central extensions
Abror Khudoyberdiyev, Doston Jumaniyozov
In this paper, we study the second adjoint cohomology of the compexification of the real conformal Galilei algebras \(\mathfrak{cga}_\ell(d,\mathbb{R})\) and their central extensio…