Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11761017; 11801150) and the Science and Technology Foundation of Guizhou Province (Grant No.[2020]1Y005).
In this paper, we give an explicit and systematic study on the double constructions of Frobenius Hom-algebras and introduce the close relations between $\mathcal{O}$-operators and Hom-dendriform algebras. Furthermore, we study the double constructions of Connes cocycles in terms of Hom-dendriform algebras. Finally, we give a clear analogy between antisymmetric infinitesimal Hom-bialgebras and Hom-dendriform $D$-bialgebras.
