24 citations · 101 across the 42 of their papers we have counts for
17 papers · 1 filter
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…
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 …
A short proof that the free associative algebra is Hopfian
Alexei Kanel-Belov, Louis Rowen, Jie-Tai Yu
A short proof is given of the fact that various classes of algebras including the free associative algebra are Hopfian, i.e., every epimorphism is an automorphism. This further sim…
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…
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…
Stable tameness of automorphisms of F<x,y,z> fixing z
Alexei Belov, Jie-Tai Yu
It is proved that every z-automorphism (z-coordinate, respectively) of the free associative algebra F<x,y,z> over an arbitrary field F is stably tame.
Applications of degree estimate for subalgebras
Yun-Chang Li, Jie-Tai Yu
Let be a field of positive characteristic and be the free algebra of rank two over . Based on the degree estimate done by Y.-C. Li and J.-T. Yu, we extend the resu…
Degree estimate for subalgebras
Yunchang Li, Jie-Tai Yu
Based on Bergman's Lemma on centralizers, we obtain a sharp lower degree bound for nonconstant elements in a subalgebra generated by two elements of a free associative algebra over…
Isomorphisms between quantum groups and
Li-Bin Li, Jie-Tai Yu
Let be a field and suppose are not roots of unity. We prove that the two quantum groups and …
Test elements, retracts and automorphic orbits
Sheng-Jun Gong, Jie-Tai Yu
Let be a free associative or polynomial algebra of rank two over a field of characteristic zero. Based on the degree estimate of Makar-Limanov and J.-T.Yu, we prove: 1) A…
Degree estimate for commutators
Vesselin Drensky, Jie-Tai Yu
Let K<X> be a free associative algebra over a field K of characteristic 0 and let each of the noncommuting polynomials f,g generate its centralizer in K<X>. Assume that the leading…
Cancellation conjecture for free associative algebras
Vesselin Drensky, Jie-Tai Yu
We develop a new method to deal with the Cancellation Conjecture of Zariski in different environments. We prove the conjecture for free associative algebras of rank two. We also pr…
Coordinates and Automorphisms of Polynomial and Free Associative Algebras of Rank Three
Vesselin Drensky, Jie-Tai Yu
We study z-automorphisms of the polynomial algebra K[x,y,z] and the free associative algebra K<x,y,z> over a field K, i.e., automorphisms which fix the variable z. We survey some r…
Automorphic equivalence problem for free associative algebras of rank two
Vesselin Drensky, Jie-Tai Yu
Let K<x,y> be the free associative algebra of rank 2 over an algebraically closed constructive field of any characteristic. We present an algorithm which decides whether or not two…
Tame Automorphisms Fixing a Variable of Free Associative Algebras of Rank Three
Vesselin Drensky, Jie-Tai Yu
We study automorphisms of the free associative algebra K<x,y,z> over a field K which fix the variable z. We describe the structure of the group of z-tame automorphisms and derive a…
The strong Anick conjecture is true
Vesselin Drensky, Jie-Tai Yu
Recently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra K<x,y,z> over a field K of characteristic 0…
Automorphisms fixing a variable of K<x,y,z>
Vesselin Drensky, Jie-Tai Yu
We study automorphisms of the free associative algebra K<x,y,z> over a field K which fix z and such that the images of x, y are linear with respect to x, y. We prove that some of t…