Redirected from "ordinary equivariant cohomology".
Statement
Let be a free associative unital algebra with some set of generators over a field . Then the centralizer or any nonscalar element is isomorphic to for some nonscalar element
As a corollary, any two commuting elements in may be presented as values of two polynomials over on the same element in .
Literature
This has been conjectured by P. M. Cohn and proved in
George M. Bergman, Centralizers in free associative algebras, Trans. Amer. Math. Soc. 137:327–344 (1969) doi
A proof using quantization is in
Alexei Kanev Belov?, Farrokh Razavinia, Wenchao Zhang, Bergman’s centralizer theorem and quantization, Communications in Algebra 46:5 (2018) doiarXiv:1708.04802
A combinatorial approach is in chapter 3 of
Zlil Sela, Noncommutative algebraic geometry, I: Monomial equations with a single variable, Model theory 3:3 (2024) 733–800 doi