an:01682850
Zbl 0977.22005
Havl????ek, M.; Klimyk, A. U.; Po??ta, S.
Central elements of the algebras \(U'_q(\text{so}_m)\) and \(U_q(\text{iso}_m)\)
EN
Czech. J. Phys. 50, No. 1, 79-84 (2000).
00081889
2000
j
22E45
single polynomial; Casimir element; root of unity
Summary: The aim of this paper is to give a set of central elements of the algebras \(U'_q(\text{so}_m)\) and \(U_q(\text{iso}_m)\) when \(q\) is a root of unity. They surprisingly arise from a single polynomial Casimir element of the algebra \(U'_q(\text{so}_3)\). 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 \(U'_q(\text{so}_m)\) and \(U_q (\text{iso}_m)\) when \(q\) is a root of unity.