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

Xiaoyuan Zhu, Honghua Hao & Bin Xin

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

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhuxy@zuel.edu.cn (Xiaoyuan Zhu)

xinbin@gznu.edu.cn (Bin Xin)

  • BibTex
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  • 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
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