Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2022, Volume 214, Pages 107–126
DOI: https://doi.org/10.36535/0233-6723-2022-214-107-126 (Mi into1065) 		 
Polynomial automorphisms, quantization, and Jacobian conjecture related problems. II. Quantization proof of Bergman's centralizer theorem

A. M. Elisheva, A. Ya. Belova, F. Razaviniaa, Yu Jie-Taib, Wenchao Zhangc

a Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
b Shenzhen University
c Huizhou University
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DOI: https://doi.org/10.36535/0233-6723-2022-214-107-126
Abstract: The purpose of this review is the collection and systematization of results concerning the quantization approach to the some classical aspects of non-commutative algebras, especially to the Jacobian conjecture. We start with quantization proof of Bergman centralizing theorem, then discourse authomorphisms of INd-schemes authomorphisms, then go to aproximation issues. Last chapter dedicated to relations between $PI$-theory Burnside type theorems and Jacobian Conjecture (Jagzev approach). This issue contains the second part of the work. The first part is: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 213 (2022), pp. 110–144. Continuation will be published in future issues.
Keywords: automorphism, quantization, Jacobian conjecture.
Funding agency Grant number
Russian Science Foundation 22-11-00177
This work was supported by the Russian Science Foundation (project No.~22-11-00177).
Document Type: Article
UDC: 512.7
MSC: 14R10, 18G85
Language: English
Citation: A. M. Elishev, A. Ya. Belov, F. Razavinia, Yu Jie-Tai, Wenchao Zhang, “Polynomial automorphisms, quantization, and Jacobian conjecture related problems. II. Quantization proof of Bergman's centralizer theorem”, Algebra, Geometry, and Combinatorics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 214, VINITI, Moscow, 2022, 107–126
Citation in format AMSBIB
\Bibitem{EliBelRaz22}
\by A.~M.~Elishev, A.~Ya.~Belov, F.~Razavinia, Yu~Jie-Tai, Wenchao~Zhang
\paper Polynomial automorphisms, quantization, and Jacobian conjecture related problems. II. Quantization proof of Bergman's centralizer theorem
\inbook Algebra, Geometry, and Combinatorics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 214
\pages 107--126
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1065}
\crossref{https://doi.org/10.36535/0233-6723-2022-214-107-126}
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