Quantum differentials on cross product Hopf algebras (Q2197780)

As the authors note, ``a modern quantum groups approach to noncommutative geometry starts with differential structures on quantum groups or Hopf algebras and associated comodule algebras, expressed in the form of a differential graded algebra (DGA)''. Actually, in general there are many such DGA's on a given Hopf algebra. In the paper under review, the authors construct canonical strongly bicovariant differential graded algebra structures on all four flavours of cross product Hopf algebras: a double cross product, a double cross coproduct, bicoproduct and bicrossproduct on the assumption that the factors have strongly bicovariant calculi.