H^(cop)—模代数和量子扬—巴克斯特模的线性映射

The Linear Maps of H^(cop)-module Algebra and Quantum Yang-Baxter Modules

设H是域k上的具有双射反极S的Hopf代数 ,M ,N是在左—右量子扬—巴克斯特模。通过讨论量子扬—巴克斯特模的同态加群 ,证明 :( 1 )当H是交换Hopf代数时 ,HOMH (M ,N)是在左—右量子扬—巴克斯特模。 ( 2 )HOMK (M ,N) ,是左—右量子扬—巴克斯特模 ;( 3)证明了ENDK (M)是Hcop—模代数 ,并且是量子扬—巴克斯特模范畴中的代数。

Let H be a Hopf algebra over field k with bijective antipode S, and fix left-right quantum Yang-Baxter modules M and N,the additive group of homomorphism Hom(M,N) is discussed, and the following are proved:(1) When H is commutative Hopf algebra, HOM H(M,N) is a left-right quantum Yang-Baxter modules;(2) HOM k(M,N) is a left-right quantum Yang-Baxter modules;(3) END K(M) is a H cop -module algebra and algebra in left-right quantum Yang-Baxter module category.