| Global dimension of weak smash product |
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| 作者姓名： | JIA Ling LI Fang |
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| 作者单位： | Department of Mathematics，Zhejiang University，Hangzhou 310027，China |
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| 基金项目： | Project supported by the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China (No. 704004), the Program for New Century Excellent Talents in Univer-sity (No. 04-0522), and the Natural Science Foundation of Zhejiang Province (No. 102028), China |
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| 摘 要： | INTRODUCTION In (Auslander, 1995), the author established the relationship of homological dimension between skew group algebra ΛG and Λ. Recall from Corollary 4.7 and Corollary 4.10 in (Auslander, 1995) that gl.dim(ΛG)=gl.dim(Λ) where ΛG is a skew group algebra with the order of G invertible in Λ. Recently, more and more mathematicians have studied homological dimension for Hopf algebra. Yang (2002) gave the relationship of homological dimension between smash product algebra A#H…
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| 关 键 词： | 弱Hopf代数学 有限空间 抽象代数 代数学 |
| 收稿时间： | 2005-10-20 |
| 修稿时间： | 2006-07-21 |
Global dimension of weak smash product |
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| JIA Ling LI Fang.Global dimension of weak smash product[J].Journal of Zhejiang University Science,2006,7(12):2088-2092. |
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| Authors: | Ling Jia Fang Li |
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| Institution: | (1) Department of Mathematics, Zhejiang University, Hangzhou, 310027, China |
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| Abstract: | In Artin algebra representation theory there is an important result which states that when the order of G is invertible in Λ then gl.dim(ΛG)=gl.dim(Λ). With the development of Hopf algebra theory, this result is generalized to smash product algebra. As known, weak Hopf algebra
is an important generalization of Hopf algebra. In this paper we give the more general result, that is the relation of homological
dimension between an algebra A and weak smash product algebra A#H, where H is a finite dimensional weak Hopf algebra over a field k and A is an H-module algebra.
Project supported by the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of
China (No. 704004), the Program for New Century Excellent Talents in University (No. 04-0522), and the Natural Science Foundation
of Zhejiang Province (No. 102028), China |
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| Keywords: | Weak Hopf algebra Weak smash product Gobal dimension |
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