On braided tensor categories of type BCD
On braided tensor categories of type BCD
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DOI：
10.1515/crll.2005.2005.581.31
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发表时间：
2003-01
期刊：
影响因子：
--
通讯作者：
Imre Tuba;H. Wenzl
中科院分区：
文献类型：
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作者：
Imre Tuba;H. Wenzl
本文对Grothendieck半环为Rep（O（∞））（形式上）、Rep（O（N））、Rep（Sp（N））或与之相关的融合范畴之一的辫子半单张量范畴进行了完全分类。如果编织是不对称的，它们完全由特定编织态射的本征值确定，并且我们精确地确定在各种情况下哪些值可以出现。如果类别允许对称编织，则其基本上由对应于矢量表示的对象的维度确定。
Abstract We give a full classification of all braided semisimple tensor categories whose Grothendieck semiring is the one of Rep(O(∞)) (formally), Rep(O(N)), Rep(Sp(N)) or of one of its associated fusion categories. If the braiding is not symmetric, they are completely determined by the eigenvalues of a certain braiding morphism, and we determine precisely which values can occur in the various cases. If the category allows a symmetric braiding, it is essentially determined by the dimension of the object corresponding to the vector representation.