The Grothendieck rings of Wu–Liu–Ding algebras and their Casimir numbers (I)

Abstract

Wu–Liu–Ding algebras are a class of affine prime regular Hopf algebras of GK-dimension one, denoted by [Formula: see text]. In this paper, we consider their quotient algebras [Formula: see text] which are a new class of non-pointed semisimple Hopf algebras. We describe the Grothendieck rings of [Formula: see text] when [Formula: see text] is odd. It turns out that the Grothendieck rings are commutative rings generated by three elements subject to some relations. Then we compute the Casimir numbers of the Grothendieck rings for [Formula: see text] and [Formula: see text].