Braided coaddition on the quantized braided matrices

Abstract

An additive braided coproduct (also be called braided coaddition) is introduced on the quantized braided matrices (QBMs). It gives QBMs another braided-Hopf algebra structure. The coaddition is also shown to be compatible with the existing coproduct such that they together form a so-called quantized-braided ring. And some quantized braided differential operator bialgebras (Hopf algebras) relating to this braided coaddition are constructed. These give a unification and generalization of the known results about braided and quantum matrices. Moreover, the coaddition construction and the related differential calculi on the QBMs are further extended to a kind of more general quantum matrix algebraic systems. Some examples are also given.