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数学进展 - 2018, Vol. 47(2): 201-206
研究论文
弱Hopf作用的余挠维数和FP投射维数
Cotorsion Dimensions and FP-projective Dimensions of Weak Hopf Actions

陈笑缘
CHEN Xiaoyuan

浙江商业职业技术学院, 杭州, 浙江, 310053
Zhejiang Business College, Hangzhou, Zhejiang, 310053, P. R. China

出版日期: 2018-05-16
2018, Vol. 47(2): 201-206
DOI: 10.11845/sxjz.2016098b


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摘要 令$H$是有限维弱Hopf代数,$A$是$H$-模代数. 本文主要讨论了$A\sharp H$和$A$的余挠维数以及FP投射维数的关系.作为主要结果的应用我们给出了几个使得${\rm LCD}(A\sharp H)= {\rm LCD}(A)$和${\rm LFPD}(A\sharp H)={\rm LFPD}(A)$的条件.
关键词 余挠维数FP-投射维数弱Hopf代数    
Abstract:Let $H$ be a finite dimensional weak Hopf algebra and $A$ be an $H$-module algebra. In this paper we mainly discuss the relations of cotorsion dimension and FP-projective dimension between $A\sharp H$ and $A$. As applications we also give the sufficient conditions for ${\rm LCD}(A\sharp H)= {\rm LCD}(A)$ and ${\rm LFPD}(A\sharp H)={\rm LFPD}(A)$.
Key wordscotorsion dimension    FP-projective dimension    weak Hopf algebra
PACS:  O153.6  
基金资助:国家自然科学基金(No. 11571037).
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[1] 侯波,张子龙,蔡炳苓. 弱Hopf代数上的对角交叉积和左右冲积 (英)[J]. 数学进展, 2012, 41(3): 320-334.
[2] 郑乃峰;. 弱Hopf代数上的Smash双积(英文)[J]. 数学进展, 2009, 38(5): 553-565.
[3] 侯波;王志玺;. 半拟三角弱Hopf代数(英文)[J]. 数学进展, 2008, 37(2): 181-188.
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