The Projective Class Rings of a family of pointed Hopf algebras of Rank two

In this paper, we compute the projective class rings of the tensor product H-n(q) = A(n)(q) circle times A(n)(q(-1)) of Taft algebras A(n)(q) and A(n)(q(-1)), and its co-cycle deformations H-n(0, q) and H-n(1, q), where n > 2 is a positive integer and q is a primitive n-th root of unity. It is shown that the projective class rings r(p)(H-n(q)), r(p)(H-n(0, q)) and r(p)(H-n(1,q)) are commutative rings generated by three elements, three elements and two elements subject to some relations, respectively. It turns out that even H-n(q), H-n(0, q) and H-n(1, q) are cocycle twist-equivalent to each other, they are of different representation types: wild, wild and tame, respectively.