Double Constructions of Frobenius Hom-Algebras and Connes Cocycles
Received:September 11, 2019  Revised:September 05, 2020
Key Word: Frobenius Hom-algebras   Hom-dendriform algebras   $\mathcal{O}$-operators   antisymmetric infinitesimal Hom-bialgebras   Hom-dendriform $D$-bialgebras
Fund ProjectL: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).
 Author Name Affiliation Shuangjian GUO School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guizhou 550025, P. R. China Lihong DONG College of Mathematics and Information Science, Henan Normal University, Henan 453007, P. R. China
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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.