Cohomology of Oriented Tree Diagram Lie Algebras

doi:10.1080/00927870802278966

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	Cohomology of Oriented Tree Diagram Lie Algebras
	Luo, Li
	2009
发表期刊	COMMUNICATIONS IN ALGEBRA
ISSN	0092-7872
卷号	37 期号:3 页码:965-984
摘要	Xu introduced a family of root-tree-diagram nilpotent Lie algebras of differential operators, in connection with evolution partial differential equations. We generalized his notion to more general oriented tree diagrams. These algebras are natural analogues of the maximal nilpotent Lie subalgebras of finite-dimensional simple Lie algebras. In this article, we use Hodge Laplacian to study the cohomology of these Lie algebras. The total rank conjecture and b2-conjecture for the algebras are proved. Moreover, we find the generating functions of the Betti numbers by means of Young tableaux for the Lie algebras associated with certain tree diagrams of single branch point. By these functions and Euler-Poincare principle, we obtain analogues of the denominator identity for finite-dimensional simple Lie algebras. The result is a natural generalization of the Bott's classical result in the case of special linear Lie algebras.
关键词	Cohomology Nilpotent Lie algebra Tree diagram
DOI	10.1080/00927870802278966
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000263869900015
出版者	TAYLOR & FRANCIS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/8994
专题	中国科学院数学与系统科学研究院
通讯作者	Luo, Li
作者单位	Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Luo, Li. Cohomology of Oriented Tree Diagram Lie Algebras[J]. COMMUNICATIONS IN ALGEBRA,2009,37(3):965-984.
APA	Luo, Li.(2009).Cohomology of Oriented Tree Diagram Lie Algebras.COMMUNICATIONS IN ALGEBRA,37(3),965-984.
MLA	Luo, Li."Cohomology of Oriented Tree Diagram Lie Algebras".COMMUNICATIONS IN ALGEBRA 37.3(2009):965-984.