论文标题
统一分类的全面累积和主要标准的完全积极性
Complete Positivity of Comultiplication and Primary Criteria for Unitary Categorification
论文作者
论文摘要
在本文中，我们研究了子因子和单一融合类别的量子傅立叶分析。我们证明了对子因子的共同授权的完全积极性，并得出了多率环的单一分类的主要$ n $ criterion。当$ n \ geq3 $时，它比Schur产品标准强。主要标准可以转换为各种标准，即使对于非交通，高级，高级，多率的多率环也更容易在实践中检查。更重要的是，主要标准可以定位在稀疏集中，因此它适用于具有稀疏已知数据的多率环。我们提供了许多例子来说明这些标准的效率和力量。
In this paper, we investigate quantum Fourier analysis on subfactors and unitary fusion categories. We prove the complete positivity of the comultiplication for subfactors and derive a primary $n$-criterion of unitary categorifcation of multifusion rings. It is stronger than the Schur product criterion when $n\geq3$. The primary criterion could be transformed into various criteria which are easier to check in practice even for noncommutative, high-rank, high-multiplicity, multifusion rings. More importantly, the primary criterion could be localized on a sparse set, so that it works for multifusion rings with sparse known data. We give numerous examples to illustrate the efficiency and the power of these criteria.
