A GENERALIZED DRINFELD QUANTUM DOUBLE CONSTRUCTION BASED ON WEAK HOPF ALGEBRAS

摘要

Let B and H be weak Hopf algebras with bijective antipodes S-B and S-H, respectively. Based on a compatible weak Hopf dual pairing (B, H, sigma), we construct a generalized Drinfeld quantum double ID(B, H) which is a weak T-coalgebra over a twisted semi-direct square of groups. In particular, when B and H are finite dimensional and the above pairing map sigma is nondegenerate, ID(B, H) admits a nontrivial quasitriangular structure. Some explicit examples are given as an application of our theory.