The projective class ring of basic and split Hopf algebras (Q1306925)

The author considers finite dimensional Hopf algebras such that all the simple modules are 1-dimensional. The structure of the complexification of the projective class ring of such a Hopf algebra is described by 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 \(U_q^+({\mathfrak{sl}}_2)\) is the product of \(n-1\) copies of the dual numbers over \(\mathbb{C}\) and two copies of \(\mathbb{C}\).