Twisted Gamma-Lie algebras and their vertex operator representations
Chen, Fulin1; Tan, Shaobin2; Wang, Qing2
Source PublicationJOURNAL OF ALGEBRA
AbstractLet Gamma be a generic subgroup of the multiplicative group C* of nonzero complex numbers. We define a class of Lie algebras associated to Gamma, called twisted P-Lie algebras, which are natural generalizations of the twisted affine Lie algebras. Starting from an arbitrary even sublattice Q of Z(N) and an arbitrary finite order isometry of ZN preserving Q, we construct a family of twisted P-vertex operators acting on generalized Fock spaces which afford irreducible representations for certain twisted F-Lie algebras. As an application, this recovers a number of known vertex operator realizations for infinite dimensional Lie algebras, such as twisted affine Lie algebras, extended affine Lie algebras of type A, trigonometric Lie algebras of series A and B, unitary Lie algebras, and BC-graded Lie algebras. (C) 2014 Elsevier Inc. All rights reserved.
KeywordTwisted Gamma-Lie algebra Vertex operator representation
Funding ProjectNSF of China[11471268] ; NSF of China[11371024] ; Natural Science Foundation of Fujian Province[2013J01018] ; Fundamental Research Funds for the Central University[2013121001]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000362146600012
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Document Type期刊论文
Corresponding AuthorWang, Qing
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
Recommended Citation
GB/T 7714
Chen, Fulin,Tan, Shaobin,Wang, Qing. Twisted Gamma-Lie algebras and their vertex operator representations[J]. JOURNAL OF ALGEBRA,2015,442:202-232.
APA Chen, Fulin,Tan, Shaobin,&Wang, Qing.(2015).Twisted Gamma-Lie algebras and their vertex operator representations.JOURNAL OF ALGEBRA,442,202-232.
MLA Chen, Fulin,et al."Twisted Gamma-Lie algebras and their vertex operator representations".JOURNAL OF ALGEBRA 442(2015):202-232.
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