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Published in:
1995 | OriginalPaper | Chapter
Structure Theorems for R q [G]
Author : Anthony Joseph
Published in: Quantum Groups and Their Primitive Ideals
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
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A finite dimensional module over $$U = {U_q}({\mathfrak{g}_C})$$ has a filtration whose quotients are simple integrable highest weight modules and hence by 4.3.10 is semisimple. Thus the Hopf dual U⋆ satisfies the direct sum decomposition of 1.4.13. By 7.1.15 (ii) this is only of interest when C is of finite type as will be henceforth assumed.