广义哈格鲁普范畴的梯度扩展

IF 0.5 4区数学 Q3 MATHEMATICS

Pure and Applied Mathematics Quarterly Pub Date : 2024-01-30 DOI:10.4310/pamq.2023.v19.n5.a3

Pinhas Grossman, Masaki Izumi, Noah Snyder

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引用次数: 0

摘要

$def\Z\{mathbb{Z}}$我们用满足多项式方程的数值不变式对广义哈格鲁普范畴的某些$\Z_2$级数扩展进行分类。特别是，我们构造了一些融合范畴的新例子，包括针对所有 $n \leq 5$的 $\Z_{2n}$ 广义哈格鲁普范畴的 $\Z_2$ 等级扩展；阿塞达-哈格鲁普范畴的 $\Z_2 \times \Z_2$ 等级扩展；以及 $\Z_2 \times \Z_2$ 广义哈格鲁普范畴通过其外自动群 $A_4$ 的扩展。这个构造使用了算子代数的内定型范畴，特别是 Cuntz 代数与自由群 $\mathrm{C}^\ast$ 代数的自由乘积。

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Graded extensions of generalized Haagerup categories

$\def\Z{\mathbb{Z}}$We classify certain $\Z_2$-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: $\Z_2$-graded extensions of $\Z_{2n}$ generalized Haagerup categories for all $n \leq 5$; $\Z_2 \times \Z_2$-graded extensions of the Asaeda-Haagerup categories; and extensions of the $\Z_2 \times \Z_2$ 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 $\mathrm{C}^\ast$-algebras.

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来源期刊

Pure and Applied Mathematics Quarterly 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high-quality, original papers on all fields of mathematics. To facilitate fruitful interchanges between mathematicians from different regions and specialties, and to effectively disseminate new breakthroughs in mathematics, the journal welcomes well-written submissions from all significant areas of mathematics. The editors are committed to promoting the highest quality of mathematical scholarship.