Quasitriangular and Differential Structures on Bicrossproduct Hopf Algebras
نویسنده
چکیده
Let X = GM be a finite group factorisation. It is shown that the quantum double D(H) of the associated bicrossproduct Hopf algebra H = kM⊲◭k(G) is itself a bicrossproduct kX⊲◭k(Y ) associated to a group Y X, where Y = G×Mop. This provides a class of bicrossproduct Hopf algebras which are quasitriangular. We also construct a subgroup Y X associated to every order-reversing automorphism θ of X. The corresponding Hopf algebra kX⊲◭k(Y ) has the same coalgebra as H. Using related results, we classify the first order bicovariant differential calculi on H in terms of orbits in a certain quotient space of X.
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