| 张良云,李~强.Smash积,辫积和L-R Smash积的新对偶[J].数学研究及应用,2007,27(3):577~585 |
| Smash积,辫积和L-R Smash积的新对偶 |
| The New Dual of Smash Products, Braided Products and L-R Smash Products |
| 投稿时间：2005-08-18 修订日期：2005-11-03 |
| DOI：10.3770/j.issn:1000-341X.2007.03.017 |
| 中文关键词: 重模代数 量子Yang-Baxter模代数 Smash积 辫积 L-R Smash积. |
| 英文关键词:dimodule algebra quantum Yang-Baxter module algebra Smash product briaided product L-R Smash product. |
| 基金项目:国家自然科学基金(10571153); 中国科学博士后基金(2005037713). |
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| 中文摘要: |
| 本文主要地证明:由$H$-重模代数$A,B$构成的Smash积$A\# B$的新对偶$_H(A\# B)^0$恰好是由重模余代数$_HA^0,_HB^0$构成的Smash余积$_HA^0\times _HB^0;$如果$(H,\sigma)$是辫化Hopf代数,则新对偶$_HH^0$是右,左$H^0-$重模余代数;由量子Yang-Baxter $H$-模代数$A,B$构成的辫积$A\propto B$的新对偶$(A\propto B)^0$恰好是由量子Yang-Baxter $H$-模余代数$_HA^0, |
| 英文摘要: |
| In this paper, we prove that the new dual $_H(A\# B)^0$ of the Smash product $A\# B$ introduced by dimodule algebras $A$ and $B$ is a Smash coproduct $_HA^0\times _HB^0$ introduced by dimodule coalgebras $_HA^0$ and $_HB^0$. If $(H,\sigma)$ is a braided Hopf algebra, we show that $_HH^0$ is a right, left $H^0$-dimodule coalgebra, and then prove that the new dual $_H(A\propto B)^0$ of the braided product $A\propto B$ introduced by quantum Yang-Baxter module algebras $A$ and $B$ is a braided coproduct $_HA^0\times _HB^0$ introduced by quantum Yang-Baxter module coalgebras $_HA^0$ and $_HB^0$. An exact sequence of the new dual ${(A\natural H)_H}^0$ of the L-R Smash product $A\natural H$ is given. |
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