Action of U_q(g) on Its Positive Part U_q^+(g)  

作　　者：Zhi Hua WANG Li Bin LI 

机构地区：[1]School of Mathematics, Yangzhou University, Jiangsu 225002, P. R. China [2]Department of Mathematics, Taizhou College, Nanjing Normal University, Jiangsu 225300, P. R. China

出　　处：《Journal of Mathematical Research and Exposition》2011年第4期665-674,共10页数学研究与评论（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No.10771182)

摘　　要：In this paper, two kinds of skew derivations of a type of Nichols algebras are intro- duced, and then the relationship between them is investigated. In particular they satisfy the quantum Serre relations. Therefore, the algebra generated by these derivations and corresponding automorphisms is a homomorphic image of the Drinfeld-Jimbo quantum enveloping algebra Uq^＋（g）, which proves the Nichols algebra becomes a/gq（g）-module algebra. But the Nichols algebra considered here is exactly Uq^＋（g）, namely, the positive part of the Drinfeld-Jimbo quantum enveloping algebra Uq^＋（g）, it turns out that Uq^＋（g） is aUq^＋（g）-module algebra.In this paper, two kinds of skew derivations of a type of Nichols algebras are intro- duced, and then the relationship between them is investigated. In particular they satisfy the quantum Serre relations. Therefore, the algebra generated by these derivations and corresponding automorphisms is a homomorphic image of the Drinfeld-Jimbo quantum enveloping algebra Uq^＋（g）, which proves the Nichols algebra becomes a/gq（g）-module algebra. But the Nichols algebra considered here is exactly Uq^＋（g）, namely, the positive part of the Drinfeld-Jimbo quantum enveloping algebra Uq^＋（g）, it turns out that Uq^＋（g） is aUq^＋（g）-module algebra.

关 键 词：Nichols algebra Yetter-Drinfeld module skew derivation quantum group. 

分 类 号：O153.3[理学—数学]