赵旭安,金春花,张继敏.Kac-Moody群及其旗流形的庞加莱级数 和有理同伦型[J].数学年刊A辑,2017,38(4):461~468
Kac-Moody群及其旗流形的庞加莱级数 和有理同伦型
Poincar\'e Series and Rational Homotopy Types of Kac-Moody Groups and Their Flag Manifolds
Received: January 21, 2015  Revised: January 02, 2017
DOI:10.16205/j.cnki.cama.2017.0007
中文关键词:  Kac-Moody group, Flag manifold, Poincar
英文关键词:Kac-Moody group, Flag manifold, Poincar
基金项目:本文受到国家自然科学基金(No.11571038)的资助.
Author NameAffiliationE-mail
ZHAO Xu'an School of Mathematics, Beijing Normal University,Beijing 100875, China. zhaoxa@bnu.edu.cn 
JIN Chunhua Science and Technology on Information Assurance Laboratory, Beijing 100072, China. jinch799@163.com 
ZHANG Jimin Tianjin Baodi Specialized Secondary School, Tianjin 301800, China. zhangjimin19870606@163.com 
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中文摘要:
      研究了不定型的Kac-Moody群及其旗流形的有理上同调. 通过从庞加莱级数提取关于同调的信息, 能够决定Kac-Moody群及其旗流形的有理上同调环. 因为这些空间都是有理formal的空间, 也决定了它们的有理同伦群及有理同伦型.
英文摘要:
      In this paper, the authors study the rational cohomology rings of indefinite Kac-Moody groups and their flag manifolds. By extracting the information of cohomology from the Poincar\'{e} series, the rational cohomology rings of these spaces can be determined. Since Kac-Moody groups and their flag manifolds are rational formal, the authors also determine the rational homotopy groups and rational homotopy types.
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