TENSOR-PRODUCTS OF QUANTIZED TILTING MODULES
TENSOR-PRODUCTS OF QUANTIZED TILTING MODULES
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DOI：
10.1007/bf02096627
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发表时间：
1992-09-01
影响因子：
2.4
通讯作者：
ANDERSEN, HH
中科院分区：
文献类型：
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作者：
ANDERSEN, HH
设U（k）表示有限维单复李代数L所对应的量子化包络代数。假设量子参数是k的单位根，其阶至少为L的Coxeter数。还假设如果出现类型G2，则该顺序是奇数并且不能被3整除。我们证明了如何定义一个约化张量积的家庭F组成的有限维简单U（k）-模块是简单的L-模块的变形，并具有非零的量子维数。这与Reshetikhin-Turaev和Turaev-Wenzl的工作一起证明了（U（k），F）是一个模Hopf代数，因此产生了3-流形的不变量。也通过最近的工作Duurhus，Jakobsen和巢它导致了一个一般的拓扑量子场论。证明方法探讨了代数群的倾斜模的量化类似物。
Let U(k) denote the quantized enveloping algebra corresponding to a finite dimensional simple complex Lie algebra L. Assume that the quantum parameter is a root of unity in k of order at least the Coxeter number for L. Also assume that this order is odd and not divisible by 3 if type G2 occurs. We demonstrate how one can define a reduced tensor product on the family F consisting of those finite dimensional simple U(k)-modules which are deformations of simple L-modules and which have non-zero quantum dimension. This together with the work of Reshetikhin-Turaev and Turaev-Wenzl prove that (U(k),F) is a modular Hopf algebra and hence produces invariants of 3-manifolds. Also by recent work of Duurhus, Jakobsen and Nest it leads to a general topological quantum field theory. The method of proof explores quantized analogues of tilting modules for algebraic groups.