| Hopf代数的半单扩张与不变子环的同调维数 |
| |
| 引用本文： | 祝家贵,张良云. Hopf代数的半单扩张与不变子环的同调维数[J]. 数学学报, 2003, 46(1): 137-142. DOI: cnki:ISSN:0583-1431.0.2003-01-018 |
| |
| 作者姓名： | 祝家贵 张良云 |
| |
| 作者单位： | 1. 南京大学数学系,南京,210093;皖西学院数学系,六安,237012
2. 南京农业大学理学院,南京,210095 |
| |
| 基金项目： | 国家自然科学基金资助项目(10071035)，安徽省教委基金资助项目 |
| |
| 摘 要： | 设H是域k上的有限维Hopf代数,A是左H-模代数,AH是A的H-不变子环.假定A/AH是半单扩张且A是平坦的右AH-模.如果H*是unimodular,且存在c∈C(A),使t·c=1.我们证明了WD(AH)=WD(A)=WD(A#H).此外,如果A是投射的左及右AH-模,则有LD(AH)=LD(A)=LD(A#H).
|
| 关 键 词： | 半单扩张 不变子环 同调维数 |
| 文章编号： | 0583-1431(2003)01-0137-06 |
| 修稿时间： | 2000-08-21 |
Semisimple Extensions of Hopf Algebra and Homological Dimension of Invariants for Hopf Actions |
| |
| Jia Gui ZHU. Semisimple Extensions of Hopf Algebra and Homological Dimension of Invariants for Hopf Actions[J]. Acta Mathematica Sinica, 2003, 46(1): 137-142. DOI: cnki:ISSN:0583-1431.0.2003-01-018 |
| |
| Authors: | Jia Gui ZHU |
| |
| Affiliation: | Jia Gui ZHU(Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China)(Department of Mathematics, West Anhui University, Luan 237012, P. R. China)(E-mail: njzjg@263.net)Liang Yun ZHANG (College of Science, Nanjing Agricultural University, Nanjing 210095, P. R. China) |
| |
| Abstract: | Let H be a finite dimensional Hopf algebra acting on an algebra yl, and let AH denote the invariant subring of A and A#H the smash product. Assume that A/AH is a semisimple extension and A is a flat right AH-module. It is shown that if H* is unimodular and A has an element of trace one then WD(AH) = WD(A) = WD(A#H). Moreover, if A is a projective left and right AH-module, then LD(AH) = LD(A) = LD(A#H). |
| |
| Keywords: | Semisimple extension Invariant subring Homological dimension |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
| 点击此处可从《数学学报》浏览原始摘要信息 |
|
点击此处可从《数学学报》下载全文 |
|
