Homological Dimension of Crossed Products of Hopf Algebras

被引：0
|
作者：
王志玺
武艳辉
机构：
[1] Beijing
[2] Department of Mathematics Capital Normal University
[3] School of Basic Courses Beijing Broadcasting Institute
来源：
Communications in Mathematical Research | 2004年 / 04期
关键词：
homological dimension; weak action; crossed product;
D O I：
10.13447/j.1674-5647.2004.04.004
中图分类号：
O153 [抽象代数（近世代数）];
学科分类号：
070104 ;
摘要：
Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra. In this paper, we characterize the projectivity (injectivity) of M as a left A#σH-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σH, the crossed product, to have finite global homological dimension is given, in terms of the global homological dimension of A and the surjectivity of trace maps, provided that H is cocommutative and A is commutative.
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页码：403 / 410
页数：8
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