一些量子Borcherds超代数及其扩张（英文）

Some Quantized Borcherds Superalgebras and Their Extensions

设wU是一个关于Borcherds超代数o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b_(ik),c_(ik),g_(ik),h_(ik)(i∈I,k=1,2,…,m_i),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.

Let wU be a new weak quantized enveloping algebra associated to a Borcherds superalgebra G. Let H be a Hopf algebra. By further adding commutative group-like elements bik, cik, gik, hik （i ∈ I, k = 1, 2, … , mi） of a Hopf Mgebra H to the superalgebra wU, we define an extended superalgebra H × wU. It is a weak Hopf superalgebra under some conditions. We also obtain an extended quantized enveloping algebra by localizing H × wU with an Ore set.