Two remarks on witten'squantum enveloping algebra

In this note we describe two simple tricks derived from work of M. Artin , J. Tate and M. Van den Bergh 2] and apply them to the quantum enveloping algebra discovered by E. Witten ll] encoding duality in three dimensional Chern-Simons gauge theory with structure group SU(2). In particular, we give a more conceptual interpretation of the dichotony in the representation theory and determine all finite dimensional simple representations.