Volume 35, Issue 1
The Direct Sum Decomposition of Type $G_2$ Lie Algebra

Commun. Math. Res., 35 (2019), pp. 10-20.

Published online: 2019-12

Preview Full PDF 481 5645
Export citation

Cited by

• 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.

• Keywords

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

17C20, 17C55

zhuxy@zuel.edu.cn (Xiaoyuan Zhu)

xinbin@gznu.edu.cn (Bin Xin)

• BibTex
• RIS
• TXT
@Article{CMR-35-10, author = {Zhu , Xiaoyuan and Hao , Honghua and Xin , Bin}, title = {The Direct Sum Decomposition of Type $G_2$ Lie Algebra}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {35}, number = {1}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2019.01.02}, url = {http://global-sci.org/intro/article_detail/cmr/13470.html} }
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 -

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.

Xiao-yuan Zhu, Hong-hua Hao & Bin Xin. (2019). The Direct Sum Decomposition of Type $G_2$ Lie Algebra. Communications in Mathematical Research . 35 (1). 10-20. doi:10.13447/j.1674-5647.2019.01.02
Copy to clipboard
The citation has been copied to your clipboard