Hom-center-symmetric algebras and bialgebras

In this work, the hom-center-symmetric algebras are constructed and discussed. Their bimodules, dual bimodules and matched pairs are defined. The relation between the dual bimodules of hom-center-symmetric algebras and the matched pairs of hom-Lie algebras is established. Furthermore, the Manin triple of hom-center-symmetric algebras is given. Finally, a theorem linking the matched pairs of hom-center-symmetric algebras, the hom-center-symmetric bialgebras and the matched pairs of sub-adjacent hom-Lie algebras is provided.