| Action of ${\cal U}_q(g)$ on Its Positive Part ${\cal U}_q^ (g)$ |
| Received:October 21, 2009 Revised:April 18, 2011 |
| Key Words:
Nichols algebra Yetter-Drinfeld module skew derivation quantum group.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10771182). |
| Author Name | Affiliation | | Zhi Hua WANG | School of Mathematics, Yangzhou University, Jiangsu 225002, P. R. China
Department of Mathematics, Taizhou College, Nanjing Normal University, Jiangsu 225300, P. R. China | | Li Bin LI | School of Mathematics, Yangzhou University, Jiangsu 225002, P. R. China |
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| Abstract: |
| In this paper, two kinds of skew derivations of a type of Nichols algebras are introduced, 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 ${\cal U}_q(g),$ which proves the Nichols algebra becomes a ${\cal U}_q(g)$-module algebra. But the Nichols algebra considered here is exactly ${\cal U}_q^ (g),$ namely, the positive part of the Drinfeld-Jimbo quantum enveloping algebra ${\cal U}_q(g),$ it turns out that ${\cal U}_q^ (g)$ is a ${\cal U}_q(g)$-module algebra. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.04.011 |
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