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Central elements of the algebras \(U'_q(\text{so}_m)\) and \(U_q(\text{iso}_m)\). (English) Zbl 0977.22005
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.

MSC:
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
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