Geodesic
Structure and Representations for the Electrical Lie Algebra of Type D4
Journal of Lie theory, Tome 31 (2021) no. 4, pp. 1031-1044
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

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 $\mathfrak{e}_{D_4}$.
Classification : 17B10, 17B20, 17B65, 17B66, 17B68
Mots-clés : Electrical Lie algebras, 3-step nilpotent Lie algebra, highest weight modules, simple modules 
@article{JLT_2021_31_4_JLT_2021_31_4_a9,
     author = {D. Gao and Y. Cai and J. 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/JLT_2021_31_4_JLT_2021_31_4_a9/}
}
TY  - JOUR
AU  - D. Gao
AU  - Y. Cai
AU  - J. 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/JLT_2021_31_4_JLT_2021_31_4_a9/
ID  - JLT_2021_31_4_JLT_2021_31_4_a9
ER  - 
%0 Journal Article
%A D. Gao
%A Y. Cai
%A J. Jiang
%T Structure and Representations for the Electrical Lie Algebra of Type D4
%J Journal of Lie theory
%D 2021
%P 1031-1044
%V 31
%N 4
%U http://geodesic.mathdoc.fr/item/JLT_2021_31_4_JLT_2021_31_4_a9/
%F JLT_2021_31_4_JLT_2021_31_4_a9
D. Gao; Y. Cai; J. 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/JLT_2021_31_4_JLT_2021_31_4_a9/