Bergman’s Centralizer Theorem and quantization


We prove Bergman’s theorem on centralizers by using generic matrices and Kontsevich’s quantization method. For any field k of positive characteristics, set be a free associative algebra, then any centralizer 𝒞(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.

Communications in Algebra