Cocommutative elements form a maximal commutative subalgebra in quantum matrices

Abstract

In this paper, we prove that the subalgebras of cocommutative elements in the quantized coordinate rings of [Formula: see text], [Formula: see text] and [Formula: see text] are the centralizers of the trace [Formula: see text] in each algebra, for [Formula: see text] 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.