Extending Structures for Lie Bialgebras
Journal of Lie Theory, Tome 33 (2023) no. 3, pp. 783-798
Voir la notice de l'article provenant de la source Heldermann Verlag
Let $(\mathfrak{g}, [\cdot,\cdot], \delta_\mathfrak{g})$ be a fixed Lie bialgebra and $V$ be a vector space. In this paper, we introduce the notion of a unified bi-product of $(\mathfrak{g}, [\cdot,\cdot], \delta_\mathfrak{g})$ by $V$ and give a theoretical answer to the extending structures problem, i.e. how to classify all Lie bialgebraic structures on $E=\mathfrak{g}\oplus V$ such that $(\mathfrak{g}, [\cdot,\cdot], \delta_\mathfrak{g})$ is a Lie sub-bialgebra up to an isomorphism of Lie bialgebras whose restriction on $\mathfrak{g}$ is the identity map. Moreover, several special unified bi-products are also introduced. In particular, the unified bi-products when $\text{dim} V=1$ are investigated in detail.
Classification :
17A30, 17B62, 17B65, 17B69
Mots-clés : Lie bialgebra, extending structure
Mots-clés : Lie bialgebra, extending structure
Affiliations des auteurs :
Yanyong Hong 1
Yanyong Hong. Extending Structures for Lie Bialgebras. Journal of Lie Theory, Tome 33 (2023) no. 3, pp. 783-798. http://geodesic.mathdoc.fr/item/JOLT_2023_33_3_a5/
@article{JOLT_2023_33_3_a5,
author = {Yanyong Hong},
title = {Extending {Structures} for {Lie} {Bialgebras}},
journal = {Journal of Lie Theory},
pages = {783--798},
year = {2023},
volume = {33},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2023_33_3_a5/}
}