q-generalized (anti -) flexible algebras and bialgebras

In this work, we provide a q-generalization of flexible algebras and related bialgebraic structures, including center-symmetric (also called antiflexible) algebras, and their bialgebras. Their basic properties are derived and discussed. Their connection with known algebraic structures, previously developed in the literature, is established. A q-generalization of Myung theorem is given. Main properties related to bimodules, matched pairs and dual bimodules as well as their algebraic consequences are investigated and analyzed. Finally, the equivalence between q-generalized flexible algebras, their Manin triple and bialgebras is established.