13 citations · 33 across the 10 of their papers we have counts for
10 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…
Augmented Polynomial Symplectomorphisms and Quantization
Alexei Kanel-Belov, Andrey Elishev, Jie-Tai Yu
The objective of this paper is the proof of a conjecture of Kontsevich on the isomorphism between groups of polynomial symplectomorphisms and automorphisms of the corresponding Wey…
Noncommutative Bialynicki-Birula Theorem
Andrey Elishev, Alexei Kanel-Belov, Farrokh Razavinia +2
In this short note we prove that every maximal torus action on the free algebra is conjugate to a linear action. This statement is the free algebra analogue of a classical theorem…
Automorphisms of Weyl Algebra and a Conjecture of Kontsevich
Alexei Kanel-Belov, Andrey Elishev, Jie-Tai Yu
We outline the proof of a conjecture of Kontsevich on the isomorphism between the group of polynomial symplectomorphisms in variables and the group of automorphisms of the …
On the tame authomorphism approximation, augmentation Topology of Automorphism Groups and -schemes, and authomorphisms of tame automorphism groups
A. Kanel-Belov, J. -T. Yu, A. Elishev
We study authomorphisms of -groups of polynomial automorphisms (wich are singular) via tame approximations. Such objects were pioneeered in research by B.I.Plotkin We obtain a…
Lifting of Polynomial Symplectomorphisms and Deformation Quantization
Alexei Kanel-Belov, Sergey Grigoriev, Andrey Elishev +2
We study the problem of lifting of polynomial symplectomorphisms in characteristic zero to automorphisms of the Weyl algebra by means of approximation by tame automorphisms. We uti…
Independence of the B-KK Isomorphism of Infinite Prime
Alexei Kanel-Belov, Andrey Elishev, Jie-Tai Yu
We investigate a certain class of Ind-scheme morphisms corresponding to homomorphisms between the automorphism group of the -th complex Weyl algebra and the group of Poisson str…
On Planar Algebraic Curves and Holonomic -modules in Positive Characteristic
Alexei Kanel-Belov, Andrey Elishev
In this paper we study a correspondence between cyclic modules over the first Weyl algebra and planar algebraic curves in positive characteristic. In particular, we show that any s…
On The Zariski Topology Of Automorphism Groups Of Affine Spaces And Algebras
Alexei Kanel-Belov, Jie-Tai Yu, Andrey Elishev
We study the Zariski topology of the ind-groups of polynomial and free associative algebras $\Aut(K[x_1,...,x_n])$ (which is equivalent to the automorphism group of the affine spac…