Integrable modules for graded Lie tori with finite-dimensional weight spaces

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Pal, Souvik¹ 

[1] Harish Chandra Res Inst HBNI, Chhatnag Rd, Allahabad 211019, Uttar Pradesh, India

关键词: Lie tori;    Integrable;    Toroidal;    Highest central operators;   

DOI  :  10.1016/j.jpaa.2021.106679

来源: Elsevier

【 摘 要 】

An important problem in the representation theory of affine and toroidal Lie algebras is to classify all possible irreducible integrable modules with finite-dimensional weight spaces. Recently the irreducible integrable modules having finite-dimensional weight spaces with non-trivial central action have been classified for a more general class of Lie algebras, namely the graded Lie tori. In this paper, we classify all the irreducible integrable modules with finite-dimensional weight spaces for this graded Lie tori where the central elements act trivially. Thus we ultimately obtain all the simple objects in the category of integrable modules with finite-dimensional weight spaces for the graded Lie tori. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free