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

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• 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

• AMS Subject Headings

17C20, 17C55

zhuxy@zuel.edu.cn (Xiaoyuan Zhu)

xinbin@gznu.edu.cn (Bin Xin)

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@Article{CMR-35-10, author = {Xiaoyuan and Zhu and zhuxy@zuel.edu.cn and 5897 and School of Economics and Statistics, Guangzhou University, Guangzhou, 510006 and Xiaoyuan Zhu and Honghua and Hao and and 5898 and School of Economics and Statistics, Guangzhou University, Guangzhou, 510006 and Honghua Hao and Bin and Xin and xinbin@gznu.edu.cn and 5899 and School of Mathematics Science, Guizhou Normal University, Guiyang, 550001 and Bin Xin}, 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
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