Geodesic
Extending Structures for Lie Bialgebras
Journal of Lie theory, Tome 33 (2023) no. 3, pp. 783-798
Cet article a éte moissonné depuis la source Heldermann Verlag

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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 
@article{JLT_2023_33_3_JLT_2023_33_3_a5,
     author = {Y. 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/JLT_2023_33_3_JLT_2023_33_3_a5/}
}
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Y. Hong. Extending Structures for Lie Bialgebras. Journal of Lie theory, Tome 33 (2023) no. 3, pp. 783-798. http://geodesic.mathdoc.fr/item/JLT_2023_33_3_JLT_2023_33_3_a5/