论文标题
Sigma与Parafermion顶点操作员代数$ K（\ Mathfrak {sl} _2，K）$相关
Sigma involutions associated with parafermion vertex operator algebra $K(\mathfrak{sl}_2,k)$
论文作者
论文摘要
parafermion顶点操作员代数$ k（\ mathfrak {sl} _2，k）$的不可修复的模块，如果$ k（\ mathfrak {sl} _2，k）$ k $ k $ k $ k $ k $ k $ k的融合代数的自动形态为$σ$ -Type。对于任何整数$ k \ ge 3 $，我们表明存在订单$ 2 $ $ k（\ mathfrak {sl} _2，k）^{\langleθ\ rangle} $ spann the irreducible the ucred的$ k（\ mathfrak {sl} _2，k） $ k（\ mathfrak {sl} _2，k）$ - 模块，其中$θ$是$ k（\ mathfrak {sl} _2，k）$的互动。我们还讨论了这种自动形态的一些例子。
An irreducible module for the parafermion vertex operator algebra $K(\mathfrak{sl}_2,k)$ is said to be of $σ$-type if an automorphism of the fusion algebra of $K(\mathfrak{sl}_2,k)$ of order $k$ is trivial on it. For any integer $k \ge 3$, we show that there exists an automorphism of order $2$ of the subalgebra of the fusion algebra of $K(\mathfrak{sl}_2,k)^{\langle θ\rangle}$ spanned by the irreducible direct summands of $σ$-type irreducible $K(\mathfrak{sl}_2,k)$-modules, where $θ$ is an involution of $K(\mathfrak{sl}_2,k)$. We discuss some examples of such an automorphism as well.
