The Direct Sum Decomposition of Type $G_2$ Lie Algebra

Authors

  • Xiaoyuan Zhu School of Economics and Statistics, Guangzhou University, Guangzhou, 510006
  • Honghua Hao School of Economics and Statistics, Guangzhou University, Guangzhou, 510006
  • Bin Xin School of Mathematics Science, Guizhou Normal University, Guiyang, 550001

DOI:

https://doi.org/10.13447/j.1674-5647.2019.01.02

Keywords:

simple Lie algebra $G_2$, simple Lie algebra $A_1$, direct sum decomposition, the highest weight module

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.

Downloads

Published

2020-03-18

Issue

Vol. 35 No. 1 (2019)

Section

Articles