Near-group fusion categories and their doubles
Near-group fusion categories and their doubles
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DOI：
10.1016/j.aim.2013.12.014
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发表时间：
2012-08
期刊：
影响因子：
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通讯作者：
David E. Evans;T. Gannon
中科院分区：
文献类型：
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作者：
David E. Evans;T. Gannon
近群融合范畴是其中除了1个简单对象之外的所有简单对象都是可逆的融合范畴C。这些范畴的例子包括坦巴拉-山上范畴和D5（1）和E6子因子的偶数扇区，尽管还有无限多的其他范畴。我们对近群融合范畴进行了分类，并计算了它们的双打和与共形场论相关的模数据。除此之外，我们明确构建了40多个新的有限深度子因子，琼斯指数范围从6.85到14.93。我们期望所有这些双打实现的理性共形场论。
A near-group fusion category is a fusion category C where all but 1 simple objects are invertible. Examples of these include the Tambara–Yamagami categories and the even sectors of the D 5 (1) and E 6 subfactors, though there are infinitely many others. We classify the near-group fusion categories, and compute their doubles and the modular data relevant to conformal field theory. Among other things, we explicitly construct over 40 new finite depth subfactors, with Jones index ranging from around 6.85 to around 14.93. We expect all of these doubles to be realised by rational conformal field theories.