The Projective Class Ring of Basic and Split Hopf Algebras

We describe the structure of the complexification of the projective class ring of a basic and split Hopf algebra using a positive integer determined by the composition series of the projective cover of the trivial module. If q is a root of unity of order n, the projective class algebra of u_q⁺(sl₂) is the product of n–1 copies of the dual numbers over C and two copies of C.