Braided anti-flexible bialgebras

Abstract

We introduce the concept of braided anti-flexible bialgebra and construct cocycle bicrossproduct anti-flexible bialgebras. As an application, we solve the extending problem for anti-flexible bialgebras by using some non-abelian cohomology theory.Comment: 37 pages, many typos, misprints and English language errors are corrected.The proofs which contain long direct computations are shortened. Continues arXiv:2112.11977 and arXiv:2203.1569