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.

中文翻译：

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Hom-左对称双代数的一种新方法

本文的主要目的是考虑霍姆左对称双代数的新定义。还研究了共界的Hom左对称双代数。特别地，我们给出了一个必要和充分的条件，即s-矩阵是Co-条件条件下Hom- S-方程的解。