Representations for certain crossed simplicial groups generated by braided Hopf algebras
We find solutions of a nonlinear equation which provide representations for the new groups R(n) defined in . The groups are crossed simplicial groups in the sense of Loday  (Sec.6.3). These solutions are based on the Bulacu and Beattie construction of braided Hopf algebras in the category of Yetter-Drinfeld modules . We discuss the connection of these solutions with Hopf equation in a braided monoidal category (a system of mixed Yang-Baxter type equations presented in ). Generalized quantum doubles for pairs of Hopf algebras can afford weak projections.