论文标题
在$ g $ - 涂成$ \ star $ - 代数和与编织$ g $ - actions相关的融合环上
On $G$-crossed Frobenius $\star$-algebras and fusion rings associated with braided $G$-actions
论文作者
论文摘要
对于有限的$ g $，Turaev引入了编织的$ G $交叉融合类别的概念。 Etingof，Nikshych和Ostrik研究了编织$ G $ $ G $串联的编织融合类别的分类。在本文中，我们将定义$ g $ - 涂成的frobenius $ \ star $ -Algebra的概念，并给出（严格的）$ g $ - 涂成可交换性的frobenius $ \ star $ -algebra $ r $ $ r $ $ g $的$ g $的$ g $ $ g $的分类。现在，假设$ \ Mathcal {B} $是一个非脱位编织的融合类别，配备了有限组$ g $的编织操作。我们将看到，相关的$ G $ fusion戒指实际上是（严格的）$ g $ - 涂成frobenius $ \ star $ -Algebra。我们将根据Etingof，Nikshych，Ostrik的编织$ G $ ACTIONS的分类来描述此$ G $串联的融合环，并得出了一个Verlinde公式来计算其融合系数。
For a finite group $G$, Turaev introduced the notion of a braided $G$-crossed fusion category. The classification of braided $G$-crossed extensions of braided fusion categories was studied by Etingof, Nikshych and Ostrik in terms of certain group cohomological data. In this paper we will define the notion of a $G$-crossed Frobenius $\star$-algebra and give a classification of (strict) $G$-crossed extensions of a commutative Frobenius $\star$-algebra $R$ equipped with a given action of $G$, in terms of the second group cohomology $H^2(G,R^\times)$. Now suppose that $\mathcal{B}$ is a non-degenerate braided fusion category equipped with a braided action of a finite group $G$. We will see that the associated $G$-graded fusion ring is in fact a (strict) $G$-crossed Frobenius $\star$-algebra. We will describe this $G$-crossed fusion ring in terms of the classification of braided $G$-actions by Etingof, Nikshych, Ostrik and derive a Verlinde formula to compute its fusion coefficients.
