Summary: The main purpose of this paper is to consider a new definition of Hom-left-symmetric bialgebra. The coboundary Hom-left-symmetric bialgebra is also studied. In particular, we give a necessary and sufficient condition that $s$-matrix is a solution of the Hom-$S$-equation by a cocycle condition.
[13] Zhang, R., Hou, D., Bai, C.: A Hom-version of the affinizations of Balinskii-Novikov and Novikov superalgebras. J. Math. Phys. 52 (2011), Article ID 023505, 19 pages. DOI 10.1063/1.3546025 | MR 2798403 | Zbl 1314.17007