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Summary: The author gives the defining relations of a new type of bialgebras that generalize both the quantum groups and braided groups as well as the quantum supergroups. The relations of the algebras are determined by a pair of matrices $(R, Z)$ that solve a system of Yang-Baxter-type equations. The matrix coproduct and counit are of standard matrix form, however, the multiplication in the tensor product of the algebra is defined by virtue of the braiding map given by the matrix $Z$. Besides simple solutions of the system of the Yang-Baxter-type equations that generate either quantum groups or braided groups, we have found several solutions that generate genuine quantum braided groups that by a choice of parameters give quantum or braided groups as a special case. (English) |
