| 张良云,李方.关于拟三角Hopf代数的Cylinder余代数和Cylinder余积(英)[J].数学研究及应用,2006,26(4):635~648 |
| 关于拟三角Hopf代数的Cylinder余代数和Cylinder余积(英) |
| Cylinder Coalgebras and Cylinder Coproducts for Quasitriangular Hopf Algebras |
| 投稿时间：2005-03-04 |
| DOI：10.3770/j.issn:1000-341X.2006.04.001 |
| 中文关键词: 拟三角Hopf代数 cylinder余代数 cylinder余积 辫余积. |
| 英文关键词:quasitriangular Hopf algebras cylinder coalgebras cylinder coproducts braided coproducts. |
| 基金项目:国家自然科学基金(10571153) 和中国博士后科学基金(2005037713) |
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| 摘要点击次数: 3105 |
| 全文下载次数: 1861 |
| 中文摘要: |
| 本文引入两个概念,即,关于拟三角双代数的cylinder余代数和cylinder余积, 并指出存在一个反余代数同构:$(H, \overline{\Delta})\cong (H, \tilde{\Delta})$,其中$(H, \overline{\Delta})$是cylinder余积,$(H,\tilde{\Delta})$是辫余积. 对任意有限维Hopf代数$H$,我们证明Drinfel'd量子偶$(D(H),\overline{\Delta}_{D(H)})$是cylinder余积.设$(H, H, R)$是余配对Hopf代数,如果$R\in Z(H\otimes H)$,则通过两次扭曲,我们可以构造扭曲余代数$(H^{\Re})^{R^{-1}}$,它的余乘法恰是cylinder余积.而且对任意的广义Long重模,通过cylinder扭曲,我们可以构造Yang-Baxter方程,四辫对和Long方程. |
| 英文摘要: |
| This paper introduces the concepts of cylinder coalgebras and cylinder coproducts for quasitriangular bialgebras, and points out that there exists an anti-coalgebra isomorphism $(H, \overline{\Delta})\cong (H, \tilde{\Delta})$, where $(H, \overline{\Delta})$ is the cylinder coproduct, and $(H, \tilde{\Delta})$ is the braided coproduct given by Kass. For any finite dimensional Hopf algebra $H$, the Drinfel'd double $(D(H), \overline{\Delta}_{D(H)})$ is proved to be the cylinder coproduct. Let $(H, H, R)$ be copaired Hopf algebras. If $R\in Z(H\otimes H)$ with inverse $R^{-1}$ and skew inverse $\Re$, then the twisted coalgebra $(H^{\Re})^{R^{-1}}$ is constructed via twice twists, whose comultiplication is exactly the cylinder coproduct. Moreover, for any generalized Long dimodule, some solutions for Yang-Baxter equations, four braid pairs and Long equations are constructed via cylinder twists. |
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