We define two-parameter quantum supergroup U_(r,s)(osp(1|2n)) by generators and relations for the first time,together with the Z_2 graded Hopf algebra structure.

Hochschild(co)homology groups of Z_2×Z_2-Galois covering of exterior algebra in two variables

The author study a procedure of reconstruction of braided Hopf algebra in this paper, the main result obtained is: while f be braided Hopf algebra homomorphism, a non-commutative braided Hopf algebra can be reconstructed into a commutative braided Hopf algebra.

The crossproduct over weak Hopf algebras ;

Two-parameter weak Hopf algebraω_(r,s)~d(sl_n)is obtained by weakening the set of group-like elements of two-parameter quan- tum group U_(r.

Let H be a weak Hopf algebra and A be an H-module algebra with its invariant subalgebra AH.

On cosemisimple Hopf algebras contains simple subcoalgebra of dimension p~2;

Killing form of Hopf algebras;

Co-representations of prime dimension for cosemisimple Hopf algebras;

Hopf*-algebra Structures on Some Hopf Algebras;

The convolution properties of right H-comodule algebras are studied in this paper with detailed discussions made on the sufficient and essential condition for r to be a twisting of Hopf algebras (H ,), and the effect of twisting on the structures of left H-module algebras and right H-comodule algebras A.

It is well known that Hopf algebras, YangBaxter and quantum groups are three main research directions in modern mathematics and come from three different disciplines.