On the Structure of Graded λ-Hopf Algebras  

作　　者：Jian Hua SUN Pu ZHANG 

机构地区：[1]Department of Mathematics, Yangzhou University, Yangzhou 225002, P. R. China [2]Department of Mathematics, Shanghai Jiaotong University, Shanghai 200000, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2009年第1期95-108,共14页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China;Yangzhou University Natural Science Foundation

摘　　要：Let G be an abelian group, B the G-graded λ-Hopf algebra with A being a bicharacter on G. By introducing some new twisted algebras （coalgebras）, we investigate the basic properties of the graded antipode and the structure for B. We also prove that a G-graded λ-Hopf algebra can be embedded in a usual Hopf algebra. As an application, it is given that if G is a finite abelian group then the graded antipode of a finite dimensional G-graded A-Hopf algebra is invertible.Let G be an abelian group, B the G-graded λ-Hopf algebra with A being a bicharacter on G. By introducing some new twisted algebras （coalgebras）, we investigate the basic properties of the graded antipode and the structure for B. We also prove that a G-graded λ-Hopf algebra can be embedded in a usual Hopf algebra. As an application, it is given that if G is a finite abelian group then the graded antipode of a finite dimensional G-graded A-Hopf algebra is invertible.

关 键 词：twisted algebra （coalgebra） graded Hopf algebra graded antipode 

分 类 号：O187.2[理学—数学]