一些量子Borcherds超代数及其扩张

摘要

Let wU be a new weak quantized enveloping algebra associated to a Borcherds superalgebrag.Let H be a Hopf algebra.By further adding commutative group-like elements bik,(C)ik,(g)ik,hik (i ∈ I,k =1,2,…,mi) of a Hopf algebra H to the superalgebra wU,we define an extended superalgebra H (⊕) wU.It is a weak Hopf superalgebra under some conditions.Wealso obtain an extended quantized enveloping algebra by localizing H (⊕) wU with an Ore set.%设wU是一个关于Borcherds超代数g的弱量子包络代数,H是一个Hopf代数.在代数wU中增加H的类群元素bik,(c)ik,(g)ik,hik(i∈I,k=1,2,…,mi),定义了一个扩张超代数H(⊕)wU,并证明它在一定条件下构成弱Hopf超代数.利用一个Ore集对代数H(⊕)wU进行局部化,还得到了一个扩张量子包络代数.