1Dept. of Mathematics, Jilin University, Changchun 130012, P. R. China 2College of Mathematics and Information Science, Hebei University, Baoding 071002, P. R. China
Journal of Lie Theory, Tome 30 (2020) no. 1, pp. 239-257
\newcommand{\ad}{\mathrm{ad}} Any involutive derivation $D$ on a 3-Lie algebra $A$ induces a local cocycle 3-Lie bialgebra $(A\ltimes_{\ad^*} A^*, \Delta)$. We give precise formulas of the 3-Lie algebra $((A\oplus A^*)^*, \Delta^*)$ and show that the local cocycle 3-Lie bialgebra $(A\ltimes_{\ad^*} A^*, \Delta)$ induced by the involutive derivation $D$ gives rise to a Manin triple of 3-Lie algebras. We give examples of $12$-dimensional and $16$-dimensional Manin triples using involutive derivations on certain $3$-dimensional and $4$-dimensional $3$-Lie algebras.
1
Dept. of Mathematics, Jilin University, Changchun 130012, P. R. China
2
College of Mathematics and Information Science, Hebei University, Baoding 071002, P. R. China
Shuai Hou; Ruipu Bai; Yunhe Sheng. Manin Triples of 3-Lie Algebras Induced by Involutive Derivations. Journal of Lie Theory, Tome 30 (2020) no. 1, pp. 239-257. http://geodesic.mathdoc.fr/item/JOLT_2020_30_1_a13/
@article{JOLT_2020_30_1_a13,
author = {Shuai Hou and Ruipu Bai and Yunhe Sheng},
title = {Manin {Triples} of {3-Lie} {Algebras} {Induced} by {Involutive} {Derivations}},
journal = {Journal of Lie Theory},
pages = {239--257},
year = {2020},
volume = {30},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2020_30_1_a13/}
}
TY - JOUR
AU - Shuai Hou
AU - Ruipu Bai
AU - Yunhe Sheng
TI - Manin Triples of 3-Lie Algebras Induced by Involutive Derivations
JO - Journal of Lie Theory
PY - 2020
SP - 239
EP - 257
VL - 30
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2020_30_1_a13/
ID - JOLT_2020_30_1_a13
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%J Journal of Lie Theory
%D 2020
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%U http://geodesic.mathdoc.fr/item/JOLT_2020_30_1_a13/
%F JOLT_2020_30_1_a13
