Cocommutative elements form a maximal commutative subalgebra in quantum matrices

In this paper, we prove that the subalgebras of cocommutative elements in the quantized coordinate rings of Mn, GLn and SLn are the centralizers of the trace x1,1 + ⋯ + xn,n in each algebra, for q ∈ℂ × being not a root of unity. In particular, it is not only a commutative subalgebra as it was known before, but it is a maximal one. © 2018 World Scientific Publishing Company