李群的k级整体维数及其共形例外量子子群

秩二李代数B2和G2的例外量子子群

Exceptional quantum subgroups for the rank two Lie algebras B2 and G2

李代数B2（在2，3，7，12层）和G2（在3，4层）的例外模不变量可以由共形嵌入得到.我们确定了量子对称的相关代数，并发现或恢复，作为副产品，描述特殊的量子子群类型B2或G2的编码其模块结构的相关融合范畴的图。给出了全球维度。

Level bounds for exceptional quantum subgroups in rank two

There is a long-standing belief that the modular tensor categories $\mathcal{C}(\mathfrak{g},k)$, for $k\in\mathbb{Z}_{\geq1}$ and finite-dimensional simple complex Lie algebras $\mathfrak{g}$, contain exceptional connected étale algebras at only finitely many levels $k$. This premise has known implications for the study of relations in the Witt group of nondegenerate braided fusion categories, modular invariants of conformal field theories, and the classification of subfactors in the theory of von Neumann algebras. Here we confirm this conjecture when $\mathfrak{g}$ has rank 2, contributing p…

Deducing the symmetry of the standard model from the automorphism and structure groups of the exceptional Jordan algebra

We continue the study undertaken in \cite{DV} of the exceptional Jordan algebra $J = J_3^8$ as (part of) the finite-dimensional quantum algebra in an almost classical space-time approach to particle physics. Along with reviewing known properties of $J$ and of the associated exceptional Lie groups we argue that the symmetry of the model can be deduced from the Borel-de Siebenthal theory of maximal connected subgroups of simple compact Lie groups.

特殊SU（4）模不变量的量子对称性

Quantum symmetries for exceptional SU(4) modular invariants associated with conformal embeddings

SU（4）的三个例外模不变量存在于第4、6和8层。它们可以通过适当的共形嵌入得到，并且相应的图具有自融合性。从这些嵌入，或从它们的相关模不变量，我们确定量子对称的代数，获得它们的生成元，并作为副产品，恢复已知的图E4（SU 4），E6（SU 4）和E8（SU 4）描述SU（4）型的例外量子子群。我们还得到了它们各自及其相关量子群胚的示性数（量子基数、维数）。

非例外群的量子对称共轭类

Quantum symmetric conjugacy classes of non-exceptional groups

本文研究了经典矩阵群的量子对称共轭类，计算了其与量子稳定子群的一维表示。

Type $II$ quantum subgroups of $\mathfrak{sl}_N$. $I$: Symmetries of local modules

This paper is the first of a pair that aims to classify a large number of the type $II$ quantum subgroups of the categories $\mathcal{C}(\mathfrak{sl}_{r+1},k)$. In this work we classify the braided auto-equivalences of the categories of local modules for all known type $I$ quantum subgroups of $\mathcal{C}(\mathfrak{sl}_{r+1},k)$. We find that the symmetries are all non-exceptional except for four cases (up to level-rank duality). These exceptional cases are the orbifolds $\mathcal{C}( \mathfrak{sl}_{2},16)_{\operatorname{Rep}(\mathbb{Z}_2)}$, $\mathcal{C}( \mathfrak{sl}_{3},9)_{\operatorname…