A counterpart of the Verlinde algebra for the small quantum group. (Q1421138)

Let \(\mathfrak g\) be a semisimple complex Lie algebra, \(q\) a root of unity of odd order, and \(U_q^{\text{ fin}}({\mathfrak g})\) the associated small quantum group. The author shows that the ideal spanned by the characters of projective modules in the Grothendieck ring of the category of finite-dimensional modules over \(U_q^{\text{ fin}}({\mathfrak g})\) has a description parallel to that of the Verlinde algebra of the fusion category, with the character of the Steinberg module on the role of the identity.