2-supertransitive subfactors at index 3+5
2-supertransitive subfactors at index 3+5
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2-索引 3 5 处的超传递子因子
DOI：
10.1016/j.jfa.2015.06.023
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发表时间：
2014
影响因子：
1.7
通讯作者：
David Penneys
中科院分区：
文献类型：
--
作者：
S. Morrison;David Penneys
给出了一种证明平面代数可求性的新方法。事实上，这种方法对于有限深度子因子平面代数是通用的。通过在方法的应用中做出谨慎的选择，通常可以显著降低计算的复杂性。利用我们的方法，证明了一类主图由对边长为2的菱形构成的子因子平面代数的存在唯一性，我们称之为“2D2”。预计这将是分类索引3+ 5以下的子因子平面代数所需的最后剩余构造。这种分类还需要证明主图4442的子因子平面代数的唯一性。我们包括一个简短的证明这一事实，泉知道，但尚未发表。这是arXiv: 1406.3401的已发布版本。
We introduce a new method for showing that a planar algebra is evaluable. In fact, this method is universal for finite depth subfactor planar algebras. By making careful choices in the method's application, one can often significantly reduce the complexity of the computations. Using our technique, we prove existence and uniqueness of a subfactor planar algebra with principal graph consisting of a diamond with arms of length 2 at opposite sides, which we call “2D2”. This is expected to be the last remaining construction required for the classification of subfactor planar algebras up to index 3+ 5. This classification will also require showing the uniqueness of the subfactor planar algebra with principal graph 4442. We include a short proof of this fact, known to Izumi but as yet unpublished. This is the published version of arXiv: 1406.3401.