Journal of Lie Theory

no. 1
On Hom-Pre-Lie Bialgebras
Journal of Lie Theory, Volume 31 (2021) no. 1, pp. 149-168
We introduce Hom-pre-Lie bialgebras in the general framework of the cohomology theory for Hom-Lie algebras. We show that Hom-pre-Lie bialgebras, standard Manin triples for Hom-pre-Lie algebras and certain matched pairs of Hom-pre-Lie algebras are equivalent. Due to the usage of the cohomology theory, it makes us successfully study the coboundary Hom-pre-Lie bialgebras. The notion of Hom-s-matrix is introduced, by which we can construct Hom-pre-Lie bialgebras naturally. Finally we introduce Hom-O-operators on Hom-pre-Lie algebras and Hom-L-dendriform algebras, by which we construct Hom-s-matrices.
DOI: 10.5802/jolt.1163
Classification: 16T25, 17B62, 17B99
Keywords: Hom-pre-Lie algebra, Manin triple, Hom-pre-Lie bialgebra, Hom-s-equation 
@article{JOLT_2021_31_1_a7,
     author = {S. Liu and A. Makhlouf and L. Song},
     title = {On {Hom-Pre-Lie} {Bialgebras}},
     journal = {Journal of Lie Theory},
     pages = {149--168},
     year = {2021},
     volume = {31},
     number = {1},
     doi = {10.5802/jolt.1163},
     zbl = {1472.17074},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1163/}
}
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S. Liu; A. Makhlouf; L. Song. On Hom-Pre-Lie Bialgebras. Journal of Lie Theory, Volume 31 (2021) no. 1, pp. 149-168. doi: 10.5802/jolt.1163

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