The complexity of crossed products

被引：0
|
作者：
Ling Liu
Bing-Liang Shen
机构：
[1] Zhejiang Normal University,Shanghai University of Finance and Economics
[2] Zhejiang College,undefined
来源：
Mathematical Notes | 2013年 / 93卷
关键词：
crossed product; complexity; trivial module; semisimple algebra; Sweedler’s 4-dimensional Hopf algebra;
D O I：
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学科分类号：
摘要：
Let H be a finite-dimensional Hopf algebra, let A be a finite-dimensional algebra measured by H, and let A #σH be a crossed product. In this paper, we first show that if H is semisimple as well as its dual H*, then the complexity of A #σH is equal to that of A. Furthermore, we prove that the complexity of a finite-dimensional Hopf algebra H is equal to the complexity of the trivial module Hk. As an application, we prove that the complexity of Sweedler’s 4-dimensional Hopf algebra H4 is equal to 1.
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页码：426 / 430
页数：4
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