Journal of Lie Theory

no. 4
Quasi-triangular Hom-Lie Bialgebras
Journal of Lie Theory, Volume 22 (2012) no. 4, pp. 1075-1089
Recently certain twisted Lie algebras, so-called Hom-Lie algebras, and their duals have been considered in the literature. In this paper we investigate boundary and quasi-triangular Hom-Lie bialgebras further. In particular, we characterize the quasi-triangularity of boundary Hom-Lie bialgebras in terms of both a certain Hom-Lie algebra morphism and a certain Hom-Lie coalgebra morphism. We also give a necessary and sufficient condition for a given Hom-Lie algebra and a given 2-tensor to admit a coboundary Hom-Lie bialgebra structure. Finally, we generalize the Drinfeld double of a Lie bialgebra to Hom-Lie bialgebras and discuss the dual codouble.
DOI: 10.5802/jolt.706
Classification: 16W30, 17B99, 17B37
Keywords: Hom-Lie algebra, Hom-Lie bialgebra, quasi-triangular Hom-Lie bialgebra, (co)double Hom-Lie bialgebra 
@article{JOLT_2012_22_4_a7,
     author = {Y. Chen and Z. Wang and L. Zhang},
     title = {Quasi-triangular {Hom-Lie} {Bialgebras}},
     journal = {Journal of Lie Theory},
     pages = {1075--1089},
     year = {2012},
     volume = {22},
     number = {4},
     doi = {10.5802/jolt.706},
     zbl = {1272.17026},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.706/}
}
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Y. Chen; Z. Wang; L. Zhang. Quasi-triangular Hom-Lie Bialgebras. Journal of Lie Theory, Volume 22 (2012) no. 4, pp. 1075-1089. doi: 10.5802/jolt.706

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