Bicrossed Products of Generalized Taft Algebra and Group Algebras.

Let G be a group generated by a set of finite order elements. We prove that any bicrossed product H_m,d(q) ⋈ k[G] between the generalized Taft algebra H_m,d(q) and group algebra k[G] is actually the smash product H_m,d(q)♯k[G]. Then we show that the classification of these smash products could be reduced to the description of the group automorphisms of G. As an application, the classification of H m , d (q) ⋈ k [ C n 1 × C n 2 ] is completely presented by generators and relations, where C_n denotes the n-cyclic group. [ABSTRACT FROM AUTHOR]