Cohomology of Oriented Tree Diagram Lie Algebras
文献类型：期刊论文
| 作者 | Luo, Li |
| 刊名 | COMMUNICATIONS IN ALGEBRA
 |
| 出版日期 | 2009 |
| 卷号 | 37期号:3页码:965-984 |
| 关键词 | Cohomology Nilpotent Lie algebra Tree diagram |
| ISSN号 | 0092-7872 |
| DOI | 10.1080/00927870802278966 |
| 英文摘要 | 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. |
| 语种 | 英语 |
| WOS记录号 | WOS:000263869900015 |
| 出版者 | TAYLOR & FRANCIS INC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/8993]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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