论文标题
广义Haagerup类别的分级扩展
Graded extensions of generalized Haagerup categories
论文作者
论文摘要
我们将某些$ \ Mathbb {z} _2 $ $ \ Mathbb {Z} _2 $ graded分类按满足多项式方程式的数值不变性来分类。特别是，我们构建了许多融合类别的新示例，包括：$ \ mathbb {z} _2 $ - $ \ mathbb {z} _ {2n} $ generalized haagerup类别的所有$ n \ n \ leq 5 $; $ \ mathbb {z} _2 \ times \ times \ mathbb {z} _2 $ - 加入Asaeda-haagerup类别的扩展；以及$ \ Mathbb {Z} _2 \ times \ Mathbb {z} _2 $ terlemized haagerup类别的扩展，其外部自动形态组$ a_4 $。该构建使用运算符代数的内态类别，尤其是具有免费组C $^*$代数的Cuntz代数的免费产品。
We classify certain $\mathbb{Z}_2 $-graded extensions of generalized Haagerup categories in terms of numerical invariants satisfying polynomial equations. In particular, we construct a number of new examples of fusion categories, including: $\mathbb{Z}_2 $-graded extensions of $\mathbb{Z}_{2n} $ generalized Haagerup categories for all $n \leq 5 $; $\mathbb{Z}_2 \times \mathbb{Z}_2 $-graded extensions of the Asaeda-Haagerup categories; and extensions of the $\mathbb{Z}_2 \times \mathbb{Z}_2 $ generalized Haagerup category by its outer automorphism group $A_4 $. The construction uses endomorphism categories of operator algebras, and in particular, free products of Cuntz algebras with free group C$^*$-algebras.
