13 citations · 33 across the 14 of their papers we have counts for
15 papers
Dimension-free estimates on distances between subsets of volume inside a unit-volume body
Abdulamin Ismailov, Alexei Kanel-Belov, Fyodor Ivlev
Average distance between two points in a unit-volume body tends to infinity as . However, for two small subsets of volume t…
On the chromatic numbers of 3-dimensional slices
D. D. Cherkashin, A. J. Kanel-Belov, G. A. Strukov +1
We prove that for an arbitrary holds \[ χ(\mathbb{R}^3 \times [0,\varepsilon]^6) \geq 10, \] where stands for the chromatic number of an (infinite) graph w…
Two-dimensional self-interlocking structures in three-space
Vassily O. Manturov, Alexei Kanel-Belov, Seongjeong Kim
It is well known that if there exists a finite set of convex bodies on the plane with non-overlapping interiors, then there is at least one "extremal" one among them, i.e., some on…
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…
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…
Construction of a quotient ring of in which a binomial is invertible using small cancellation methods
A. Atkarskaya, A. Kanel-Belov, E. Plotkin +1
We apply small cancellation methods originating from group theory to investigate the structure of a quotient ring , where $\mathbb{Z}_2\mathc…
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…
Periodicity of Rauzy Scheme for substitution words
Alexei Kanel-Belov, Ivan Mitrofanov
From Rauzy graph Rauzy Scheme can be obtaining by uniting sequence of vertices of ingoing and outgoing degree 1 by arches. This notion is a tool to describe Rauzy graph behavior. F…
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…
Periodicity of Rauzy scheme and substitutional systems
Alexei Kanel-Belov, Ivan Mitrofanov
In the paper the notion of {\em Rauzy scheme} is introduced. From Rauzy graph Rauzy Scheme can be obtaining by uniting sequence of vertices of ingoing and outgoing degree 1 by arch…
Interlocking of convex polyhedra: towards a geometric theory of fragmented solids
A. J. Kanel-Belov, A. V. Dyskin, Y. Estrin +2
We present structures comprised of identical convex polyhedra which are interlocked geometrically. These sets cannot be disassembled by removing individual polyhedra by translation…