[1]张良云,刘应安.关于可分代数的Maschke定理[J].东南大学学报(自然科学版),1999,29(2):116-120.[doi:10.3969/j.issn.1001-0505.1999.02.022]
 Zhang Liangyun,Liu Yingan.Maschke’s Theorem of Separable Algebra[J].Journal of Southeast University (Natural Science Edition),1999,29(2):116-120.[doi:10.3969/j.issn.1001-0505.1999.02.022]
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关于可分代数的Maschke定理()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
29
期数:
1999年第2期
页码:
116-120
栏目:
数学、物理学、力学
出版日期:
1999-03-20

文章信息/Info

Title:
Maschke’s Theorem of Separable Algebra
作者:
张良云1 刘应安2
1 南京农业大学理学院, 南京 210095)(2 南京林业大学,南京 210037
Author(s):
Zhang Liangyun1 Liu Yingan2
1 College of Science, Nanjing Agricultural University, Nanjing 210095
2 Nanjing Forestry University, Nanjing 210037
关键词:
可分代数 余可分余代数 双可分双代数 弱Hopf代数
Keywords:
separable algebra co-separable coalgebra bi-separable bialgebra weak Hopf algbra
分类号:
O153.3
DOI:
10.3969/j.issn.1001-0505.1999.02.022
摘要:
给出如下几个主要结论:① 设A为可分代数,则C余可分当且仅当卷积余代数A*C余可分; ② 设A为有限维半单可换Hopf代数,B为A的子Hopf代数,如果A余可分,那么Smash积#(A,B)为可分代数; ③ 设K→fHgπL,为Hopf代数的可裂短正合序列,则H余可分当且仅当K,L余可分,且当H双可分时,L也为双可分.
Abstract:
This paper primarily gives the following conclusions: ① Let A be an algebra, thus C is a coseparable coalgebra if and only if A*C is a coseparable convolution coalgebra; ② Let A be a dimensional semisimple commutative Hopf algebra and B be a sub-Hopf algebra of A. if A is a coseparable coalgebra, then smash product #(A,B) is a separable algebra; ③ Let K〖FY1〗fHgπL be a split short exact sequence of Hopf algebras, thus H is a coseparable Hopf algebra if and only if K and L are coseparable Hopf algebras, also if H is a bi-separable Hopf algebra, then L is a bi-separable Hopf algebra.

参考文献/References:

[1] Doi Y.Homological coalgebra.J Math Soc Japan,1981,33(1):31~50
[2] Montgomery S.Hopf algebras and their actions on rings.Lectures in Math.Providenc AMS:CBMS LN 82,1993.1~238
[3] 张良云.可分代数和相关Hopf模.南京师范大学学报,1998,21(2):22~24
[4] 王栓宏.H-弱余模余代数和交叉余积.数学年刊,1995,16A(4):471~479
[5] Radford D E.Coreflexive coalgebras.J Alg,1973,26:512~535
[6] Cohen M.Hopf algebra actions.J Alg,1986,100:363~379
[7] Masuoka A.Generalization of cleft comodule algebras.Comm Alg,1992,20(12):3703~3721
[8] Koppinen M.Coideal subalgebras in Hopf algebrs:freeness,integrals,smash products.Comm Alg,1993,21(2):427~444
[9] 朱胜林.有限维半单余半单Hopf代数.Comm Alg,1993,21(11):3871~3885
[10] Cohen M.From supersymetry to quantum commutativity.J Alg,1994,168:1~27
[11] Molnar R K.Semi-direct products of Hopf algebras.J Alg,1977,47:29~51
[12] 李方,张良云.弱Hopf代数和半群环上的分式环.数学半年刊,1997,14(1):98~104

备注/Memo

备注/Memo:
基金项目: 南京农业大学基金资助项目.
第一作者:男,1964年生,副教授,硕士研究生.
更新日期/Last Update: 1999-03-20