47 citations · 93 across the 10 of their papers we have counts for
11 papers
On Automorphisms of the Tame Polynomial Automorphism Group in Positive Characteristic
Alexei Belov-Kanel, Andrey Elishev, Jie-Tai Yu
In this paper we prove that over algebraically closed field of positive characteristic every automorphism of the group of origin-preserving automorphisms of the polyno…
Torus actions on free associative algebras, lifting and Białynicki-Birula type theorems
Alexei Belov-Kanel, Andrey Elishev, Farrokh Razavinia +3
We examine the problem of the linearity of an algebraic torus action in the associative setting. We prove the free algebra analog of a classical theorem of BialynickiBirula, which…
Centralizers in Free Associative Algebras and Generic Matrices
Alexei Belov-Kanel, Farrokh Razavinia, Wenchao Zhang
This paper is concerned with the completion of the proof of the Bergman centralizer theorem by using generic matrices based on our previous quantization proof \cite{KBRZh}. Additio…
Representability of affine algebras over an arbitrary field
Alexei Belov-Kanel, Louis Rowen, Uzi Vishne
In a series of papers, we used full quivers as tools in describing PI-varieties of algebras and providing a complete proof of Belov's solution of Specht's problem for affine algebr…
Specht's problem for associative affine algebras over commutative Noetherian rings
Alexei Belov-Kanel, Louis Rowen, Uzi Vishne
In a series of papers \cite{BRV1}, \cite{BRV2}, \cite{BRV3} we introduced full quivers and pseudo-quivers of representations of algebras, and used them as tools in describing PI-va…
Full quivers of representations of algebras
Alexei Belov-Kanel, Louis H. Rowen, Uzi Vishne
We introduce the notion of the full quiver of a representation of an algebra, which is a cover of the (classical) quiver, but which captures properties of the representation itself…
Structure of Zariski-closed algebras
Alexei Belov-Kanel, Louis H. Rowen, Uzi Vishne
The objective of this paper is to describe the structure of Zariski closed algebras, which provide a useful generalization to finite dimensional algebras in the study of representa…
On the lifting of the Nagata automorphism
Alexei Belov-Kanel, Jie-Tai Yu
It is proved that the Nagata automorphism (Nagata coordinates, respectively) of the polynomial algebra over a field cannot be lifted to a -automorphism (-coord…
Automorphisms of the endomorphism semigroup of a free commutative algebra
A. Belov-Kanel, R. Lipyanski
We describe the automorphism group of the endomorphism semigroup $\End(K[x_1,...,x_n])$ of ring of polynomials over an {\it arbitrary} field . A similar result…
The Jacobian Conjecture is stably equivalent to the Dixmier Conjecture
Alexei Belov-Kanel, Maxim Kontsevich
The Jacobian conjecture in dimension asserts that any polynomial endomorphism of -dimensional affine space over a field of zero characteristic, with the Jacobian equal 1, is…
Automorphisms of the Weyl algebra
Alexei Belov-Kanel, Maxim Kontsevich
We discuss a conjecture which says that the automorphism group of the Weyl algebra in characteristic zero is canonically isomorphic to the automorphism group of the corresponding P…