Differential calculuses on the quantized braided groups

Abstract

Braided differential calculuses on the quantized braided groups are constructed and their braided bialgebra (Hopf algebra) structures are demonstrated. These are a kind of generalization and unification of the differential calculuses on quantum groups, braided groups, quantum supergroups, etc., and contain the latter ones as special cases. Moreover, it is shown that some quantum differential (co)vector algebras are covariant under the braided “local” coactions of the obtained braided differential bialgebras (Hopf algebras). Some examples are also given.