Jones–Witten Invariants for Nonsimply Connected Lie Groups and the Geometry of the Weyl Alcove
Jones–Witten Invariants for Nonsimply Connected Lie Groups and the Geometry of the Weyl Alcove
复制标题
非单连通李群的 Jones-Witten 不变量和 Weyl Alcove 几何
DOI：
10.1006/aima.1999.1910
复制
发表时间：
1999
影响因子：
1.7
通讯作者：
S. Sawin
中科院分区：
文献类型：
--
作者：
S. Sawin
摘要利用Muger和Bruguieres的商过程，从单李代数的Weyl凹室的闭子集中构造模范畴和TQFT。特别是，它是确定在哪些水平上与非单连通群相关的闭子集导致TQFT。这些TQFT中的许多被示出为分解成来自较小子集的TQFT的张量积。其中的“素”子集进行了分类，除了一些给定的TQFT取决于所描述的村上，Ohtsuki和冈田的同源性，他们被证明是在一对一的对应关系与TQFT预测Dijkgraaf和维滕与陈-西蒙斯理论与非单连通李群。因此，特别是一个严格的构造Dijkgraaf-Witten TQFT。作为一个副产品，一个纯粹的量子群证明的模块性的完整的Weyl凹室的任意量子群在任意水平。
Abstract The quotient process of Muger and Bruguieres is used to construct modular categories and TQFTs out of closed subsets of the Weyl alcove of a simple Lie algebra. In particular it is determined at which levels closed subsets associated to nonsimply connected groups lead to TQFTs. Many of these TQFTs are shown to decompose into a tensor product of TQFTs coming from smaller subsets. The “prime” subsets among these are classified, and apart from some giving TQFTs depending on homology as described by Murakami, Ohtsuki and Okada, they are shown to be in one-to-one correspondence with the TQFTs predicted by Dijkgraaf and Witten to be associated to Chern–Simons theory with a nonsimply connected Lie group. Thus in particular a rigorous construction of the Dijkgraaf–Witten TQFTs is given. As a byproduct, a purely quantum groups proof of the modularity of the full Weyl alcove for arbitrary quantum groups at arbitrary levels is given.
DOI：
--
发表时间：
2005
期刊：
影响因子：
--
作者：
T. Kobayashi;T. Oshima
通讯作者：
T. Oshima
DOI：
10.1007/978-1-4612-9839-7
发表时间：
1971
期刊：
--
影响因子：
--
作者：
S. Lane
通讯作者：
S. Lane