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pro vyhledávání: '"Umirbaev, Ualbai"'
Autor:
Umirbaev, Ualbai
We show that every automorphism of a free metabelian Lie algebra $M_n$ of rank $n\geq 4$ over an arbitrary field $K$ is almost tame, that is, it is a product of so-called Chein automorphisms (or one-row transformations). Moreover, we show that the gr
Externí odkaz:
http://arxiv.org/abs/2406.12884
Autor:
Umirbaev, Ualbai
The well-known Bachmuth-Mochizuki-Roman'kov Theorem \cite{BM,Romankov85} states that every automorphism of the free metabelian group of rank $\geq 4$ is tame. In 1992 Yu. Bahturin and S. Nabiyev \cite{BN} claimed that every nontrivial inner automorph
Externí odkaz:
http://arxiv.org/abs/2401.07182
Autor:
Ismailov, Nurlan, Umirbaev, Ualbai
We construct a finite-dimensional metabelian right-symmetric algebra over an arbitrary field that does not have a finite basis of identities.
Comment: 16 pages
Comment: 16 pages
Externí odkaz:
http://arxiv.org/abs/2311.17758
The Veronese subalgebra $A_0$ of degree $d\geq 2$ of the polynomial algebra $A=K[x_1,x_2,\ldots,x_n]$ over a field $K$ in the variables $x_1,x_2,\ldots,x_n$ is the subalgebra of $A$ generated by all monomials of degree $d$ and the Veronese subalgebra
Externí odkaz:
http://arxiv.org/abs/2307.07823
We show that free algebras of the variety of algebras generated by the Witt algebra $W_n$, the left-symmetric Witt algebra $L_n$, and the symplectic Poisson algebra $P_n$ can be described as subalgebras of differential polynomial algebras with respec
Externí odkaz:
http://arxiv.org/abs/2301.06693
Autor:
Aitzhanova, Bakhyt, Umirbaev, Ualbai
We prove that every derivation and every locally nilpotent derivation of the subalgebra $K[x^n, x^{n-1}y,\ldots,xy^{n-1}, y^n]$, where $n\geq 2$, of the polynomial algebra $K[x,y]$ in two variables over a field $K$ of characteristic zero is induced b
Externí odkaz:
http://arxiv.org/abs/2210.12781
In this paper, we study Novikov algebras satisfying nontrivial identities. We show that a Novikov algebra over a field of zero characteristic that satisfies a nontrivial identity satisfies some unexpected "universal" identities, in particular, right
Externí odkaz:
http://arxiv.org/abs/2209.13662
Autor:
Dotsenko, Vladimir, Umirbaev, Ualbai
All algebras of a certain type are said to form a Nielsen-Schreier variety if every subalgebra of a free algebra is free. This property has been perceived as extremely rare; in particular, only six Nielsen-Schreier varieties of algebras with one bina
Externí odkaz:
http://arxiv.org/abs/2205.05364
Autor:
Ismailov, Nurlan, Umirbaev, Ualbai
Publikováno v:
In Journal of Algebra 15 November 2024 658:759-778
We prove that any Novikov algebra over a field of characteristic $\neq 2$ is Lie-solvable if and only if its commutator ideal $[N,N]$ is right nilpotent. We also construct examples of infinite-dimensional Lie-solvable Novikov algebras $N$ with non ni
Externí odkaz:
http://arxiv.org/abs/2112.13457