Central elements of the algebras $U_q^{\prime }({\mathrm{so}}_m)$ and $U_q({\mathrm{iso}}_m)$

Abstract

The aim of this paper is to give a set of central elements of the algebras $U_q^{\prime }({\mathrm{so}}_m)$ and $U_q({\mathrm{iso}}_m)$ when q is a root of unity. They are surprisingly arise from a single polynomial Casimir element of the algebra $U_q^{\prime }({\mathrm{so}}_3)$. 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 $U_q^{\prime }({\mathrm{so}}_m)$ and $U_q({\mathrm{iso}}_m)$ when q is a root of unity.

6 pages, LaTaX

References in corpus (2)

• q-Deformed Orthogonal and Pseudo-Orthogonal Algebras and Their Representations
• Representations of the q-deformed algebra $U_q({\mathrm{iso}}_2)$

Cited by in corpus (3)

• Coideal subalgebras in quantum affine algebras
• Some interactions between Hopf Galois extensions and noncommutative rings
• Twisted WZW Branes from Twisted REA's