Tree diagram Lie algebras of differential operators and evolution partial differential equations
文献类型：期刊论文
| 作者 | Xu, Xiaoping
|
| 刊名 | JOURNAL OF LIE THEORY
 |
| 出版日期 | 2006 |
| 卷号 | 16期号:4页码:691-718 |
| 关键词 | tree diagram Lie algebra of differential operators abelian ideal evolution partial differential equation Campbell-Hausdorff formula |
| ISSN号 | 0949-5932 |
| 英文摘要 | A tree diagram is a tree with positive integral weight on each edge, which is a notion generalized from the Dynkin diagrams of finite-dimensional simple Lie algebras. We introduce two nilpotent Lie algebras and their extended solvable Lie algebras associated with each tree diagram. The solvable tree diagram Lie algebras turn out to be complete Lie algebras of maximal rank analogous to the Borel subalgebras of finite-dimensional simple Lie algebras. Their abelian ideals are completely determined. Using a high-order Campbell-Hausdorff formula and certain abelian ideals of the tree diagram Lie algebras, we solve the initial value problem of first-order evolution partial differential equations associated with nilpotent tree diagram Lie algebras and high-order evolution partial differential equations, including heat conduction type equations related to generalized Tricomi operators associated with trees. |
| 语种 | 英语 |
| WOS记录号 | WOS:000241680500004 |
| 出版者 | HELDERMANN VERLAG |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/2961]  |
| 专题 | 数学所 |
| 通讯作者 | Xu, Xiaoping |
| 作者单位 | Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Xu, Xiaoping. Tree diagram Lie algebras of differential operators and evolution partial differential equations[J]. JOURNAL OF LIE THEORY,2006,16(4):691-718. |
| APA | Xu, Xiaoping.(2006).Tree diagram Lie algebras of differential operators and evolution partial differential equations.JOURNAL OF LIE THEORY,16(4),691-718. |
| MLA | Xu, Xiaoping."Tree diagram Lie algebras of differential operators and evolution partial differential equations".JOURNAL OF LIE THEORY 16.4(2006):691-718. |
入库方式： OAI收割
来源：数学与系统科学研究院
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