代数$U'_q({\rm so}_m)$和$U_q({\rm iso}_m)$的中心元
Central elements of the algebras $U'_q({\rm so}_m)$ and $U_q({\rm iso}_m)$
摘要：
本文的目的是给出当q是单位根时，代数$U'_q({\rm so}_m)$和$U_q({\rm iso}_m)$的一组中心元.令人惊讶的是，它们是由代数$U'_q({\rm so}_3)$的一个多项式卡西米尔元产生的。证明了当q为单位根时，这些代数在任意q值下（不仅q为单位根）的Casimir元和q为单位根的中心元生成$U'_q({\rm so}_m)$和$U_q({\rm iso}_m)$的中心.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
