Deformed Kac-Moody algebras and their representations
文献类型：期刊论文
| 作者 | Liu, Jianbo2; Zhao, Kaiming1 |
| 刊名 | JOURNAL OF ALGEBRA
 |
| 出版日期 | 2008-06-01 |
| 卷号 | 319期号:11页码:4692-4711 |
| 关键词 | deformed Kac-Moody algebra invariant symmetric bilinear form lowest (respectively highest) weight Verma module irreducible module |
| ISSN号 | 0021-8693 |
| DOI | 10.1016/j.jalgebra.2008.01.009 |
| 英文摘要 | A class of Lie algebras S (A) associated to generalized Cartan matrices A is studied. The Lie algebras S(A) have much simpler structure than Kac-Moody algebras, but have the same root spaces with g(A). In particular, S(A) has an abelian subalgebra of "half size." We show that, S(A) has a non-degenerate invariant symmetric bilinear form if and only if A is symmetrizable; S(X-1) congruent to S(X-2) if and only if the GCMs X-1 and X-2 are the same up to a permutation of rows and columns. We study the lowest (respectively highest) weight Verma module (V) over bar(lambda) (respectively (V) over tilde (lambda)) over S(A), and obtain the necessary and sufficient conditions for (V) over bar(lambda) to be irreducible, and also find its maximal proper submodule when (V) over bar(lambda) is reducible. Then using graded dual module of (V) over bar(lambda) we deduce the necessary and sufficient conditions for (V) over tilde (lambda) to be irreducible. (C) 2008 Elsevier Inc. All rights reserved. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000256283200012 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/5707]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Zhao, Kaiming |
| 作者单位 | 1.Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada 2.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Liu, Jianbo,Zhao, Kaiming. Deformed Kac-Moody algebras and their representations[J]. JOURNAL OF ALGEBRA,2008,319(11):4692-4711. |
| APA | Liu, Jianbo,&Zhao, Kaiming.(2008).Deformed Kac-Moody algebras and their representations.JOURNAL OF ALGEBRA,319(11),4692-4711. |
| MLA | Liu, Jianbo,et al."Deformed Kac-Moody algebras and their representations".JOURNAL OF ALGEBRA 319.11(2008):4692-4711. |
入库方式： OAI收割
来源：数学与系统科学研究院
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