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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:
 2.2e+46 Representations of Lie and linear algebraic groups over real fields: analytic methods
##### Keywords:
single polynomial; Casimir element; root of unity
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