论文标题
单倍体代数$ C^*$ - 张量类别和Schellekens列表
Haploid algebras in $C^*$-tensor categories and the Schellekens list
论文作者
论文摘要
我们证明，$ C^*$ - Tensor类别中的单倍体联想代数$ \ MATHCAL {C} $等同于Q-System（一个特殊的$ C^*$ - FROBENIUS代数），$ \ MATHCAL {C} $ IF且仅在刚性时，这使我们能够证明所有70个强烈理性的霍明型顶点操作员代数的单位性具有中央电荷$ C = 24 $和非零重量的子空间，对应于所谓的Schellekens列表中的1-70个条目。此外，使用这些顶点操作员代数的最新广义深孔构造，我们证明它们在腕表，川岛，朗戈和韦纳的意义上也是强烈的本地，因此我们获得了一些与列表条目相关的新的圆锥形结合网。最后，我们完全对单一$ n = 1 $和$ n = 2 $ super-virasoro virasoro顶点操作员超级级别的Superalgebra扩展进行了完全分类，并分别依靠已知的分类级别的超级conconification-SuperConcement。
We prove that a haploid associative algebra in a $C^*$-tensor category $\mathcal{C}$ is equivalent to a Q-system (a special $C^*$-Frobenius algebra) in $\mathcal{C}$ if and only if it is rigid. This allows us to prove the unitarity of all the 70 strongly rational holomorphic vertex operator algebras with central charge $c=24$ and non-zero weight-one subspace, corresponding to entries 1-70 of the so called Schellekens list. Furthermore, using the recent generalized deep hole construction of these vertex operator algebras, we prove that they are also strongly local in the sense of Carpi, Kawahigashi, Longo and Weiner and consequently we obtain some new holomorphic conformal nets associated to the entries of the list. Finally, we completely classify the simple CFT type vertex operator superalgebra extensions of the unitary $N=1$ and $N=2$ super-Virasoro vertex operator superalgebras with central charge $c<\frac{3}{2}$ and $c<3$ respectively, relying on the known classification results for the corresponding superconformal nets.
