Projective class ring of a restricted quantum group Uq(sl*2)

In this paper, we compute the projective class ring of the new type restricted quantum group Uq(sl*2). First, we describe the principal indecomposable projective Uq(sl*2)-modules and study their radicals, composition series, Cartan matrix of Uq(sl*2) and so on. Then, we deconstruct the tensor products between two simple modules, two indecomposable projective modules and a simple module and an indecomposable projective module, into direct sum of some indecomposable representations. At last, we characterize the projective class ring by generators and relations explicitly.