On the center of quantized enveloping algebras
\textit{V. G. Drinfeld} gave a construction of central elements of a ribbon Hopf algebra \(U\) [Leningr. Math. J. 1, 321-342 (1990; Zbl 0718.16035)]. These elements also appear in \textit{N. Reshetikhin}'s work on invariants of tangles [Leningr. Math. J. 1, 491-513 (1990; Zbl 0715.17016)]. When \(U = U_{q}(g)\) is a quantized universal enveloping algebra, this construction can also be performed and is related with the description of the center in terms of the decomposition of the adjoint representation of \(U_{q}(g)\) [\textit{A. Joseph} and \textit{G. Letzter}, Am. J. Math. 116, 127-177 (1994; Zbl 0811.17007)]; or with respect to the quantum Harish-Chandra homomorphism [\textit{M. Rosso}, Ann. Sci. Éc. Norm. Supér. (4) 23, 445-467 (1990; Zbl 0721.17012)]. In the present paper, a nice formula relating some of these central elements for \(U_{q}(g)\) is given. As an application, a statement of [\textit{L. Faddeev, N. Reshetikhin} and \textit{L. Takhtadyan}, Leningr. Math. J. 1, 193-225 (1990; Zbl 0715.17015)] concerning the center of \(U_{q}(g)\) (\(g\) of type A, B, C, D) is proved.
scientific article; zbMATH DE number 1203914
scientific article