On the Center of Quantized Enveloping Algebras

Abstract

LetUbe a quasitriangular Hopf algebra. One may use theR-matrix ofUin order to construct scalar invariants of knots. Analogously, Reshetikhin wrote down tangle invariants which take their values in the center ofU. Reshetikhin's expressions thus define central elements inU. We prove here an identity characterizing some of these elements, whenUis a quantized enveloping algebra. As an application, we give a proof for a statement of Faddeev, Reshetikhin, and Takhtadzhyan concerning the center of a quantized enveloping algebra. © 1998 Academic Press.