On planar algebraic curves and holonomic 𝒟-modules in positive characteristic

Belov-Kanel, Alexei; Elishev, Andrey

doi:10.1142/s0219498816501553

Cited by 4 publications

(2 citation statements)

References 11 publications

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“…Some progress toward resolution of the B-KKC independence problem has been made recently in [10,11], although the general unconditional case is still open.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

On the augmentation topology of automorphism groups of affine spaces and algebras

Kanel-Belov

Elishev

2018

Int. J. Algebra Comput.

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“…Some progress toward resolution of the B-KKC independence problem has been made recently in [10,11], although the general unconditional case is still open.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

On the augmentation topology of automorphism groups of affine spaces and algebras

Kanel-Belov

Elishev

2018

Int. J. Algebra Comput.

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“…One direction in the Conjecture 1.3 -namely the construction of a lagrangian subvariety from a given holonomic module -has been accomplished by Bitoun [16] and, independently, Van den Bergh [17], who gave a conceptually different proof. Also, the one-dimensional case of Conjecture 1.3 was studied in [3].…”

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confidence: 99%

Lifting of polynomial symplectomorphisms and deformation quantization

Kanel-Belov

Grigoriev

Elishev

et al. 2018

Communications in Algebra

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The objective of this paper is the proof of a conjecture of Kontsevich [1] on the isomorphism between groups of polynomial symplectomorphisms and automorphisms of the corresponding Weyl algebra in characteristic zero. The proof is based on the study of topological properties of automorphism Ind-varieties of the so-called augmented and skew augmented versions of Poisson and Weyl algebras. Approximation by tame automorphisms as well as a certain singularity analysis procedure is utilized in the construction of the lifting of augmented polynomial symplectomorphisms, after which specialization of the augmentation parameter is performed in order to obtain the main result.

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Polynomial Automorphisms, Deformation Quantization and Some Applications on Noncommutative Algebras

et al. 2022

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This paper surveys results concerning the quantization approach to the Jacobian Conjecture and related topics on noncommutative algebras. We start with a brief review of the paper and its motivations. The first section deals with the approximation by tame automorphisms and the Belov–Kontsevich Conjecture. The second section provides quantization proof of Bergman’s centralizer theorem which has not been revisited for almost 50 years and formulates several related centralizer problems. In the third section, we investigate a free algebra analogue of a classical theorem of Białynicki-Birula’s theorem and give a noncommutative version of this famous theorem. Additionally, we consider positive-root torus actions and obtain the linearity property analogous to the Białynicki-Birula theorem. In the last sections, we introduce Feigin’s homomorphisms and we see how they help us in proving our main and fundamental theorems on screening operators and in the construction of our lattice Wn-algebras associated with sln, which is by far the simplest known approach concerning constructing such algebras until now.

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On planar algebraic curves and holonomic 𝒟-modules in positive characteristic

Cited by 4 publications

References 11 publications

On the augmentation topology of automorphism groups of affine spaces and algebras

On the augmentation topology of automorphism groups of affine spaces and algebras

Lifting of polynomial symplectomorphisms and deformation quantization

Polynomial Automorphisms, Deformation Quantization and Some Applications on Noncommutative Algebras

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