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.
Shanshan Liu
1
;
Abdenacer Makhlouf
2
;
Lina Song
1
1
Dept. of Mathematics, Jilin University, Changchun 130012, P. R. China
2
IRIMAS -- Dép. de Mathématiques, University of Haute Alsace, Mulhouse, France
Shanshan Liu; Abdenacer Makhlouf; Lina Song. On Hom-Pre-Lie Bialgebras. Journal of Lie Theory, Tome 31 (2021) no. 1, pp. 149-168. http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a7/
@article{JOLT_2021_31_1_a7,
author = {Shanshan Liu and Abdenacer Makhlouf and Lina Song},
title = {On {Hom-Pre-Lie} {Bialgebras}},
journal = {Journal of Lie Theory},
pages = {149--168},
year = {2021},
volume = {31},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a7/}
}
TY - JOUR
AU - Shanshan Liu
AU - Abdenacer Makhlouf
AU - Lina Song
TI - On Hom-Pre-Lie Bialgebras
JO - Journal of Lie Theory
PY - 2021
SP - 149
EP - 168
VL - 31
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a7/
ID - JOLT_2021_31_1_a7
ER -
%0 Journal Article
%A Shanshan Liu
%A Abdenacer Makhlouf
%A Lina Song
%T On Hom-Pre-Lie Bialgebras
%J Journal of Lie Theory
%D 2021
%P 149-168
%V 31
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a7/
%F JOLT_2021_31_1_a7
