WEIGHT PROPERTY FOR IDEALS OF U_q(sl(2))

Abstract

Let k be an arbitrary field of characteristic zero, and U be the quantized enveloping algebra U _q (sl(2)) over k. The aim of this present paper is to study the ideals of U at q not a root of unity. It turns out that every non-zero ideal of U can be generated by at most two highest weight vectors under the adjoint action, and by a sum of two highest weight vectors. This weight property make it possible to give a complete list of all prime (primitive, maximal) ideals of U according to their generators.

ACKNOWLEDGMENTS

The authors are sincerely grateful to Professors S. X. Liu, S. Z. Li for many stimulating comments and helpful suggestions. They also would like to thank Professors K. Q. Feng, H. J. Fang, C. R. Cai, J. Xiao, J. Y. Guo for several discussions. The paper was finally written during the stay of the first author in Department of Mathematics at University of Bielefeld. He is indebted to Professor C. M. Ringel for his kind hospitality and continuous encouragement. Supported by the National Natural Science Foundation of China and the Young Teachers' Projects from the Chinese Education Ministry.