|
|||||
|
|
| L-R smash products for bimodule algebras | |
| 引用本文： | ZHANG Liangyun. L-R smash products for bimodule algebras[J]. 自然科学进展(英文版), 2006, 16(6): 580-587. DOI: 10.1080/10020070612330038 |
| 作者姓名： | ZHANG Liangyun |
| 作者单位： | 1. Department of Mathematics, Nanjing Agricultural University, Nanjing 210095, China; 2. Department of Mathematics, Nanjing University, Nanjing 210008, China |
| 基金项目： | 中国科学院资助项目;中国博士后科学基金 |
| 摘 要： | In this paper, we prove that the L-R smash product AH is exactly the twisted smash product A＊H if H is a finite dimensional cocommutative Hopf algebra, and give a sufficient and necessary condition for L-R smash products to be bialgebras (Hopf algebras). For any finite dimensional coquasitriangular Hopf algebra (H,σ), we prove that the L-R smash product HH is semisimple Artinian if H is semisimple and H* is unimodular. In particular, the L-R smash product D(H)*D(H)* semisimple Artinian if the Drinfel’d double D(H) is semisimple. |
| 关 键 词： | bimodule algebras L-R smash products coquasitriangular Hopf algebras Long bialgebras. |
L-R smash products for bimodule algebras |
|
| ZHANG Liangyun. L-R smash products for bimodule algebras[J]. Progress in Natural Science, 2006, 16(6): 580-587. DOI: 10.1080/10020070612330038 | |
| Authors: | ZHANG Liangyun |
| Affiliation: | Department of Mathematics, Nanjing Agricultural University, Nanjing 210095, China;Department of Mathematics, Nanjing University, Nanjing 210008, China |
| Abstract: | In this paper, we prove that the L-R smash product A (＃)H is exactly the twisted smash product A * H if H is a finite dimensional cocommutative Hopf algebra, and give a sufficient and necessary condition for L-R smash products to be bialgebras (Hopf algebras). For any finite dimensional coquasitriangular Hopf algebra (H, σ), we prove that the L-R smash product H (＃)H is semisimple Artinian if H is semisimple and H* is unimodular. In particular, the L-R smash product D(H) * (＃)D(H) * semisimple Artinian if the Drinfel' d double D(H) is semisimple. |
| Keywords: | bimodule algebras L-R smash products coquasitriangular Hopf algebras Long bialgebras |
| 本文献已被 CNKI 万方数据 等数据库收录！ | |
| 点击此处可从《自然科学进展(英文版)》浏览原始摘要信息 | |
| 点击此处可从《自然科学进展(英文版)》下载全文 | |