Classifying Bicrossed Products Of Two Generalized Taft Algebras

On the basis of the theory of bicrossed product,a Hopf algebra E can factorize through Hopf algebra A and B iff the bicrossed product of A and B is isomorphic to E.In this thesis,we classify all Hopf algebras which factor through two generalized Taft algebras T_n,dn（?）and T_m,dm（q）.Firstly,we describe all possible matched pairs between two generalized Taft algebras T_n,dn（?）and T_m,dm（q）according to the quantity relation-ships among the n,d_n,m,d_m,? and q.Secondly,we get two kinds of matched pairs and the corresponding generating elements and relations.It can be roughly divided into two types:T_n,dn,m,dm^β（?,q）and Q_m^c（q）.Finally,according to the matched pairs of the bicrossed product of two generalized Taft algebras,we analyse the Hopf isomorphismψdeter-mined by quadruple（u,p,r,v）.We can get the number of isomorphism classes which factor through two generalized Taft algebras T_n,dn（?）and T_m,dm（q）:?_n,dn,m,dm^?,q.And their automorphism groups Aut_{Hop f}(T_n,dn,m,dm^β（?,q）).