[1]高姗,钟立楠*.May谱序列某些直和项[J].延边大学学报(自然科学版),2019,45(01):11-14.
　GAO Shan,ZHONG Linan*.Direct sum summand of May spectral sequence[J].Journal of Yanbian University,2019,45(01):11-14.
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May谱序列某些直和项

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 第45卷 期数: 2019年01期 页码: 11-14 栏目: 基础科学研究 出版日期: 2019-02-20
Title:
Direct sum summand of May spectral sequence
文章编号:
1004-4353(2019)01-0011-04
作者:
高姗1;  钟立楠2*
( 1.太原工业学院, 山西 太原 030008; 2.延边大学 理学院, 吉林 延吉 133002 )
Author(s):
GAO Shan1;  ZHONG Linan2*
( 1.Taiyuan Institute of Technology,Taiyuan 030008, China; 2.College of Science, Yanbian University, Yanji 133002, China )
关键词:
May谱序列;  上同调;  稳定同伦群
Keywords:
May spectral sequence;  cohomology;  stable homotopy group
分类号:
O154
文献标志码:
A
摘要:
计算了Dykin图为An的李代数的正根系上同调的一些非零直和项.首先列出了R6的全部权子复形,然后利用链同构关系的相关定理对权子复形进行了分类.最后通过对分类权子空间秩的计算,得出了R6的模3系数的上同调的所有非零直和项.本文的研究结果补充了文献[4]的相关结论.
Abstract:
In this paper, we compute some non-zero direct sum summand of the cohomology of the positive system of the Lie algebra with Dynkin graph. First we list all of the weight subcomplexes of R6 are established, then theroems about chain isomorphism are used to classify this weight subcomplexes. Finally, through the calculation of the rank of the weight subcomplexes, all of the nonzero direct sum summand of the cohomology of R6 are obtained. The research results supplement the related results of the literature [4].

参考文献/References:


[1] ADAMS J F. On the structure and application of the Steenrod algebra[J]. Math Helv, 1958,32:180-247.
[2] ZHENG Qibing. Graphs and the(co)homology of Lie algebras[EB/OL].(2011-07-01)[2012-12-11]. http:arxiv.org/abs/1107.0235.
[3] MAY J P. The cohomology of restricted Lie algebras and of Hopf algebras[J]. Journal of Algebra, 1966(3):123-145.
[4] 陆俊杰.关于May谱序列E2项的若干结果[D].天津:南开大学,2007.
[5] DWYER W G. Homology of integral upper-triangular matrices[J]. Proceedings of the American Mathematical Society, 1985,94:523-528.
[6] 高姗.May谱序列某些直和项上同调的计算[J].南开大学学报(自然科学版),2013,46(5):29-36.

备注/Memo

收稿日期: 2018-11-25
基金项目: 国家自然科学基金资助项目(11261062)
*通信作者: 钟立楠(1982—),女,博士,副教授,研究方向为代数拓扑.

更新日期/Last Update: 2019-05-20