Irreducible modules of toroidal Lie algebras arising from f?-coordinated modules of vertex algebras

被引：0
作者：
Chen, Fulin [1 ]
Li, Huansheng [2 ]
Yu, Nina [1 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
[2] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China
来源：
JOURNAL OF ALGEBRA | 2022年 / 611卷
基金：
中国国家自然科学基金;
关键词：
Toroidal Lie algebra; Vertex algebra; f(?)-coordinated module; Highest weight module; INTEGRABLE REPRESENTATIONS; QUASIFINITE REPRESENTATIONS; CLASSIFICATION;
D O I：
10.1016/j.jalgebra.2022.08.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, for every E is an element of Z, we introduce an extension of the 2-toroidal Lie algebra by certain derivations. Based on the Phi(is an element of)-coordinated modules theory for vertex algebras, we give an explicit realization of a class of irreducible highest weight modules for this extended toroidal Lie algebra. When E = 1, this affords a realization of certain irreducible modules for the toroidal extended affine Lie algebras first constructed by Billig. (C) 2022 Elsevier Inc. All rights reserved.
引用
收藏
页码：110 / 148
页数：39
相关论文
共 34 条
[1]  
Allison B., 1997, Mem. Am. Math. Soc., V603, P122
[2]  
[Anonymous], 2002, Contemp. Math.
[3]   φ∈-Coordinated modules for vertex algebras [J].
Bai, Chengming ;
Li, Haisheng ;
Pei, Yufeng .
JOURNAL OF ALGEBRA, 2015, 426 :211-242
[4]   Irreducible representations for toroidal Lie algebras [J].
Berman, S ;
Billig, Y .
JOURNAL OF ALGEBRA, 1999, 221 (01) :188-231
[5]  
Berman S., 2002, CONT MATH, V297, P1
[6]   Jet modules [J].
Billig, Yuly .
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2007, 59 (04) :712-729
[7]   Representations of toroidal extended affine Lie algebras [J].
Billig, Yuly .
JOURNAL OF ALGEBRA, 2007, 308 (01) :252-269
[8]  
Billig Y, 2006, INT MATH RES NOTICES, V2006
[9]   NEW UNITARY REPRESENTATIONS OF LOOP-GROUPS [J].
CHARI, V ;
PRESSLEY, A .
MATHEMATISCHE ANNALEN, 1986, 275 (01) :87-104
[10]  
Chen F., ARXIV
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