FINITE DIMENSIONAL REPRESENTATIONS OF u-HOPF ALGEBRAS

Abstract

Splitting trace modules of u-Hopf algebras are characterized. As an example, all finite dimensional splitting trace modules of the restricted form U_t (sl ₂) are classified. The semisimplicity of a representation V from that of tensor product V ⊗ M in _H M for u-Hopf algebra H is given.

ACKNOWLEDGMENTS

This work partially was done while the author studied in University of Bielefeld. The author would like to express his gratitude to Prof. C. M. Ringel for his hospitality and help. He also express his gratitude to Prof. J. Xiao for encouragement. Finally, he would like to thank the referee for helpful comments.