Deformed Kac-Moody algebras and their representations

doi:10.1016/j.jalgebra.2008.01.009

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	Deformed Kac-Moody algebras and their representations
	Liu, Jianbo 2; Zhao, Kaiming 1
	2008-06-01
发表期刊	JOURNAL OF ALGEBRA
ISSN	0021-8693
卷号	319 期号:11 页码:4692-4711
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.
关键词	deformed Kac-Moody algebra invariant symmetric bilinear form lowest (respectively highest) weight Verma module irreducible module
DOI	10.1016/j.jalgebra.2008.01.009
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000256283200012
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/5708
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.