The Grothendieck rings of Wu-Liu-Ding algebras and their Casimir numbers (II)

摘要

Wu-Liu-Ding algebras, that is D(m, d, xi), are a class of non-pointed affine prime regular Hopf algebras of GK-dimension one. In this paper, we mainly study a class of quotient algebras of D(m, d, xi), denoted by D'(m, d, xi), which are 2m(2)d-dimensional non-pointed semisimple Hopf algebras. For a better understanding of the structure of the Hopf algebra D'(m, d, xi), we have considered the Grothendieck rings of D'(m, d, xi) and their Casimir numbers when d is odd in our previous paper. In this paper we continue dealing with the more complex case when d is even. It turns out that the Grothendieck rings of D'(m, d, xi) are generated by four elements subject to some relations. Then we give the Casimir numbers of the Grothendieck rings of D'(1, d, xi) and D'(2, d, xi).