1School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, P. R. China 2Dept. of Mathematics, Soochow University, Suzhou, Jiangsu, P. R. China
Journal of Lie Theory, Tome 31 (2021) no. 4, pp. 1031-1044
We prove the dimension conjecture for electrical Lie algebra $\mathfrak{e}_{D_4}$ of type $D_4$. Moreover, we present a new method to construct $3$-step nilpotent Lie algebras and show that $\mathfrak{e}_{D_4}$ is isomorphic to the semidirect product of $\mathfrak{s}\mathfrak{l}_2$ with a $3$-step nilpotent Lie algebra constructed from the colored complete bipartible graph $K_{2,2}$. Also, we classify all simple highest weight modules for $\mathfrak{e}_{D_4}$.
1
School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, P. R. China
2
Dept. of Mathematics, Soochow University, Suzhou, Jiangsu, P. R. China
Dongfang Gao; Yan-an Cai; Jin Jiang. Structure and Representations for the Electrical Lie Algebra of Type D4. Journal of Lie Theory, Tome 31 (2021) no. 4, pp. 1031-1044. http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a9/
@article{JOLT_2021_31_4_a9,
author = {Dongfang Gao and Yan-an Cai and Jin Jiang},
title = {Structure and {Representations} for the {Electrical} {Lie} {Algebra} of {Type} {D\protect\textsubscript{4}}},
journal = {Journal of Lie Theory},
pages = {1031--1044},
year = {2021},
volume = {31},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a9/}
}
TY - JOUR
AU - Dongfang Gao
AU - Yan-an Cai
AU - Jin Jiang
TI - Structure and Representations for the Electrical Lie Algebra of Type D4
JO - Journal of Lie Theory
PY - 2021
SP - 1031
EP - 1044
VL - 31
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a9/
ID - JOLT_2021_31_4_a9
ER -
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%J Journal of Lie Theory
%D 2021
%P 1031-1044
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%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a9/
%F JOLT_2021_31_4_a9
