Central elements of the algebras $U'_q({\rm so}_m)$ and $U_q({\rm iso}_m)$

Abstract

The aim of this paper is to give a set of central elements of the algebras $U'_q({\rm so}_m)$ and $U_q({\rm iso}_m)$ when q is a root of unity. They are surprisingly arise from a single polynomial Casimir element of the algebra $U'_q({\rm so}_3)$. It is conjectured that the Casimir elements of these algebras under any values of q (not only for q a root of unity) and the central elements for q a root of unity derived in this paper generate the centers of $U'_q({\rm so}_m)$ and $U_q({\rm iso}_m)$ when q is a root of unity.