论文标题
组理论融合类别中的代数结构
Algebraic structures in group-theoretical fusion categories
论文作者
论文摘要
Ostrik（2003）和Natale（2017）表明，尖锐的融合类别中的扭曲组代数集合充当此类类别中不可分解的可分离代数的显式莫里塔等效类代表。我们通过在群体理论融合类别中构建明确的莫里塔等效类代表来概括这一结果。这是通过将Fuctor $φ$从Fusion类别提供到原始类别中（Frobenius）单体结构中的双模型类别来实现的。然后，我们感兴趣的代数被构建为$φ$下的扭曲组代数的图像。我们还表明，扭曲的群体代数在尖锐的融合类别中接受了弗罗贝尼乌斯代数的结构，因此，我们的代数是群体理论融合类别中的frobenius代数。他们还享受几个好的代数属性。
It was shown by Ostrik (2003) and Natale (2017) that a collection of twisted group algebras in a pointed fusion category serve as explicit Morita equivalence class representatives of indecomposable, separable algebras in such categories. We generalize this result by constructing explicit Morita equivalence class representatives of indecomposable, separable algebras in group-theoretical fusion categories. This is achieved by providing the free functor $Φ$ from fusion category to a category of bimodules in the original category with a (Frobenius) monoidal structure. Our algebras of interest are then constructed as the image of twisted group algebras under $Φ$. We also show that twisted group algebras admit the structure of Frobenius algebras in a pointed fusion category, and as a consequence, our algebras are Frobenius algebras in a group-theoretical fusion category. They also enjoy several good algebraic properties.
