We replace the group of grouplike elements of the quantized enveloping algebra U q (g) of a
finite dimensional semisimple Lie algebra g by some regular monoid and get the weak Hopf …

In this paper, we first introduce two classes of weak Hopf algebras w^ s_ n, d wn, ds of type
s~(s= 0, 1) s (s= 0, 1), which are corresponding to generalized Taft Hopf algebras H_ n, d (q) …

The structure of weak Hopf algebras corresponding to U q (sl 2) are classified by their
algebra structure and coalgebra structure. The algebra structure of weak Hopf algebras …

Let H 8 be the unique noncommutative and noncocommutative eight dimensional semi-
simple Hopf algebra. We first construct a weak Hopf algebra H_8 H 8∼ based on H 8, then …

In this paper we define a new kind of quantized enveloping algebra of a generalized Kac–
Moody algebra. We denote this algebra by. It is a noncommutative and noncocommutative …

We define a kind of quantized enveloping algebra of a generalized Kac-Moody algebra G by
adding a generator J satisfying J m= J m− 1 for some integer m⁠. We denote this algebra by …

In a recent work, 1 quantum doubles of finite dimensional Hopf algebras and finite groups
are generalized by one of the authors to those of certain finite dimensional weak Hopf …

For a class of neither pointed nor semisimple Hopf algebras $ H_ {4n} $ of dimension $4 n $,
it is shown that they are quasi-triangular, which universal $ R $-matrices are described. The …

Abstract Let r (m 2 0) be the Green ring of the weak Hopf algebra m 2 0 corresponding to
Sweedler's 4-dimensional Hopf algebra H 2, and let Aut (R (m 2 0)) be the automorphism …

为了构造出更多的弱量子代数类, 利用弱化双参数量子群U r, sd (sl n) 的类群元集的方法,
给出双参数弱Hopf 代数ω r, sd (sl n) 的构造, 它是单参数弱Hopf 代数ω qd (sl n) 的推广 …