Journal of Lie Theory

no. 3
Extending Structures for Lie Bialgebras
Journal of Lie Theory, Volume 33 (2023) no. 3, pp. 783-798
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.
DOI: 10.5802/jolt.1306
Classification: 17A30, 17B62, 17B65, 17B69
Keywords: Lie bialgebra, extending structure 
@article{JOLT_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},
     doi = {10.5802/jolt.1306},
     zbl = {1525.17020},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1306/}
}
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Y. Hong. Extending Structures for Lie Bialgebras. Journal of Lie Theory, Volume 33 (2023) no. 3, pp. 783-798. doi: 10.5802/jolt.1306

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