6 citations · 15 across the 7 of their papers we have counts for
7 papers
Nonstandard analysis, deformation quantization and some logical aspects of (non)commutative algebraic geometry
Alexei Kanel-Belov, Alexei Chilikov, Ilya Ivanov-Pogodaev +4
This paper surveys results related to well-known works of B. Plotkin and V. Remeslennikov on the edge of algebra, logic and geometry. We start from a brief review of the paper and…
Polynomial automorphisms, quantization and Jacobian conjecture related problems
Alexei Kanel-Belov, Andrey Elishev, Farrokh Razavinia +2
The purpose of this review paper is the collection, systematization and discussion of recent results concerning the quantization approach to the Jacobian conjecture, as well as cer…
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…
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…
Bergman's Centralizer Theorem and quantization
Alexei Kanel Belov, Farrokh Razavinia, Wenchao Zhang
We prove Bergman's theorem on centralizers by using generic matrices and Kontsevich's quantization method. For any field of positive characteristics, set $A=\textbf{k…
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…