Year: 2019
Author: Xiaoyuan Zhu, Honghua Hao, Bin Xin
Communications in Mathematical Research , Vol. 35 (2019), Iss. 1 : pp. 10–20
Abstract
This article mainly discusses the direct sum decomposition of type $G_2$ Lie algebra, which, under such decomposition, is decomposed into a type $A_1$ simple Lie algebra and one of its modules. Four theorems are given to describe this module, which could be the direct sum of two or three irreducible modules, or the direct sum of weight modules and trivial modules, or the highest weight module.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2019.01.02
Communications in Mathematical Research , Vol. 35 (2019), Iss. 1 : pp. 10–20
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: simple Lie algebra $G_2$ simple Lie algebra $A_1$ direct sum decomposition the highest weight module