| 半单弱Hopf代数的作用 |
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| 引用本文： | 高楠. 半单弱Hopf代数的作用[J]. 数学研究及应用, 2008, 28(1): 25-34. DOI: 10.3770/j.issn:1000-341X.2008.01.004 |
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| 作者姓名： | 高楠 |
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| 作者单位： | Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China） |
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| 摘 要： | 令H是半单弱Hopf代数, A是左H-模代数.我们证明了正则A-模的内射维数, A#H-模A的内射维数和正则A#H-模的内射维数三者是相等的. 而且,利用H在A上的不动点代数我们给出了A是Gorenstein代数的充要条件.
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| 关 键 词： | Weak Hopf algebras Gorenstein algebras Injective dimension Weak Hopf Algebras 代数 作用 fixed action sufficient condition Gorenstein prove injective dimension regular module smash product left weak Hopf algebra |
| 收稿时间： | 2006-06-06 |
| 修稿时间： | 2007-01-16 |
Actions of Semisimple Weak Hopf Algebras |
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| GAO Nan. Actions of Semisimple Weak Hopf Algebras[J]. Journal of Mathematical Research with Applications, 2008, 28(1): 25-34. DOI: 10.3770/j.issn:1000-341X.2008.01.004 |
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| Authors: | GAO Nan |
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| Affiliation: | Department of Mathematics,Shanghai Jiao Tong University,Shanghai 200240,China |
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| Abstract: | Let H be a semisimple weak Hopf algebra,A a left H-module algebra.We prove that the injective dimension of the regular A-module is equal to the one of A as the module over the smash product A#H,and equal to the one of the regular A#H-module.Also,we give a necessary and sufficient condition for A being a Gorenstein algebra,in terms of the fixed subalgebra of A under the action of H on A. |
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| Keywords: | Weak Hopf algebras Gorenstein algebras Injective dimension. |
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