Journal of Lie Theory

no. 4
The Construction of Hom-Lie Bialgebras
Journal of Lie Theory, Volume 20 (2010) no. 4, pp. 767-783
Motivated by recent literature on Hom-Lie algebras and the construction of Lie bialgebras, we investigate the construction of Hom-Lie bialgebras as a generalization of Lie bialgebras. In this paper, we mainly show how to construct (triangular coboundary) Hom-Lie bialgebras both through Hom-Lie algebras and Hom-Lie coalgebras. As examples, we consider the construction of (triangular coboundary) Hom-Lie bialgebras on the three-dimensional Heisenberg algebra, on the split simple Lie algebra sl(2) and on E3, the three-dimensional Euclidean space.
DOI: 10.5802/jolt.619
Classification: 17B99, 17B37, 16W30
Keywords: Hom-Lie algebra, Hom-Lie module, Hom-Lie bialgebra, triangular coboundary Hom-Lie bialgebra 
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     author = {Y. Chen and Y. Wang and L. Zhang},
     title = {The {Construction} of {Hom-Lie} {Bialgebras}},
     journal = {Journal of Lie Theory},
     pages = {767--783},
     year = {2010},
     volume = {20},
     number = {4},
     doi = {10.5802/jolt.619},
     zbl = {1217.17013},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.619/}
}
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Y. Chen; Y. Wang; L. Zhang. The Construction of Hom-Lie Bialgebras. Journal of Lie Theory, Volume 20 (2010) no. 4, pp. 767-783. doi: 10.5802/jolt.619

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