Bergman’s centralizer theorem and quantization

Alexei Kanel Belov; Farrokh Razavinia; Wenchao Zhang

doi:10.1080/00927872.2017.1372462

Bergman’s centralizer theorem and quantization

Alexei Kanel Belov, Farrokh Razavinia, Wenchao Zhang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We prove Bergman’s theorem [10] on centralizers by using generic matrices and Kontsevich’s quantization method. For any field k of positive characteristics, set A = k‹x₁, . .. , x_s› be a free associative algebra, then any centralizer &(f) of nontrivial element f∈A∖k is a ring of polynomials on a single variable. We also prove that there is no commutative subalgebra with transcendent degree ≥2 of A.

Original language	English
Pages (from-to)	2123-2129
Number of pages	7
Journal	Communications in Algebra
Volume	46
Issue number	5
DOIs	https://doi.org/10.1080/00927872.2017.1372462
State	Published - 4 May 2018

Bibliographical note

Funding Information:
This work was supported by the Russian Science Foundation educational scholarship with number (No 17-11-01377) for financial support.

Funding Information:
This research was funded by the Russian Science Foundation educational scholarship with number (No 17-11-01377).

Publisher Copyright:
© 2017 Taylor & Francis.

Keywords

Bergman theorem
Kontsevich
generic matrices
quantization
star product

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10.1080/00927872.2017.1372462

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Bergman’s centralizer theorem and quantization

Abstract

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Keywords

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