| 余模的Auslander-Reiten 平移 |
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| 引用本文： | 祝家贵,黎奇升,魏丽娟.余模的Auslander-Reiten 平移[J].吉首大学学报(自然科学版),2012,33(2):1-6. |
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| 作者姓名： | 祝家贵 黎奇升 魏丽娟 |
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| 作者单位： | (1.巢湖学院数学系，安徽 合肥 238000；2.吉首大学数学与计算机科学学院，湖南 吉首 416000；3.湖南理工学院数学学院，湖南 岳阳 414000) |
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| 基金项目： | 湖南省教育厅重点科学研究项目 |
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| 摘 要： | 设Γ是域k上的余代数,对函子τ=DTr:MΓqc→MΓqc作进一步研究，其中MΓqc表示MΓ中由拟有限余表示余模确定的完全子范畴.证明了当Γ是半完备余代数时,τ是范畴f.d.M〖TXX-〗Γqc与f.d.M〖TX-〗Γqp之间的等价,其中M〖TXX-〗Γqc(M〖TX-〗Γqp)是内射(投射)稳定范畴,f.d.M〖TXX-〗Γqc(f.d.M〖TX-〗Γqp)是M〖TXX-〗Γqc(M〖TX-〗Γqp)中有限维射内射(投射)余模作成的完全子范畴.
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| 关 键 词： | 余代数 余模 转置 平移 |
Auslander-Reiten Translations for Comodules |
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| ZHU Jia-gui,LI QI-sheng,WEI Li-juan.Auslander-Reiten Translations for Comodules[J].Journal of Jishou University(Natural Science Edition),2012,33(2):1-6. |
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| Authors: | ZHU Jia-gui LI QI-sheng WEI Li-juan |
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| Institution: | (1.Department of Mathematics,Chaohu College,Hefei 238000,China;2.School of Mathematics and Computer Science,Jishou University,Jishou 416000,Hunan China;3.School of Mathematics,Hunan Institute of Science and Technology,Yueyang 414000,Hunan China) |
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| Abstract: | Let Γ be a coalgebra over a field k.Further discussion of the functor τ=DTr:MΓqc→ MΓqc is carried out,where MΓqc denotes the full subcategory of MΓ determined by the quasi-finitely copresented comodules.If Γ is a semisimple coalgebra,it is proved that the functor τ:f.d.MΓqc→ f.d.MΓqp is a categories equivalence,where MΓqc(MΓqp) is the injectively(projectively) stable category and f.d.MΓqc(f.d.MΓqp) is the full subcategory of MΓqc(MΓqp) determined by the finite dimensional injective(projective) comodules. |
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| Keywords: | coalgebra comodule transpose translation |
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