论文标题
抬高展开的量子组
Uprolling Unrolled Quantum Groups
论文作者
论文摘要
我们在一个简单的lie代数$ \ mfg $的统一限制量子组$ \ overline {u} _q^h（\ mfg）$的体重模块类别中构建了交换性（超级）代数对象的家族。我们确定它们的简单模块，并得出这些类别的条件是有限的，非分级和色带。由$ \ mfg = \ mathfrak {sl} _2 $ case中的许多示例激励，我们希望其中一些类别可以很好地比较Vertex Operator代数的模块类别。我们特别关注预期的示例，对应于Feigin和Tipunin \ cite {ft}的较高等级的三重态顶点$ w_q（r）$ w_q（r）$ w_q（r）$ w_q（r）$ w_q（r）和$ b_q（r）$代数\ cite {c1}。
We construct families of commutative (super) algebra objects in the category of weight modules for the unrolled restricted quantum group $\overline{U}_q^H(\mfg)$ of a simple Lie algebra $\mfg$ at roots of unity, and study their categories of local modules. We determine their simple modules and derive conditions for these categories being finite, non-degenerate, and ribbon. Motivated by numerous examples in the $\mfg=\mathfrak{sl}_2$ case, we expect some of these categories to compare nicely to categories of modules for vertex operator algebras. We focus in particular on examples expected to correspond to the higher rank triplet vertex algebra $W_Q(r)$ of Feigin and Tipunin \cite{FT} and the $B_Q(r)$ algebras of \cite{C1}.
