TY - JOUR
T1 - The Direct Sum Decomposition of Type $G_2$ Lie Algebra
AU - Zhu , Xiaoyuan
AU - Hao , Honghua
AU - Xin , Bin
JO - Communications in Mathematical Research 
VL - 1
SP - 10
EP - 20
PY - 2019
DA - 2019/12
SN - 35
DO - http://doi.org/10.13447/j.1674-5647.2019.01.02
UR - https://global-sci.org/intro/article_detail/cmr/13470.html
KW - simple Lie algebra $G_2$, simple Lie algebra $A_1$, direct sum decomposition, the highest weight module
AB - <p style="text-align: justify;">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.</p>