We prove Bergman’s theorem  on centralizers by using generic matrices and Kontsevich’s quantization method. For any field k of positive characteristics, set A = k‹x1, . .. , xs› 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.
Bibliographical noteFunding Information:
This work was supported by the Russian Science Foundation educational scholarship with number (No 17-11-01377) for financial support.
This research was funded by the Russian Science Foundation educational scholarship with number (No 17-11-01377).
© 2017 Taylor & Francis.
- Bergman theorem
- generic matrices
- star product