论文标题
顶点操作员超级级别的合理性具有合理的保形权重
Rationality of vertex operator superalgebras with rational conformal weights
论文作者
论文摘要
对于Aggine Vertex Algebra $ v_k（\ Mathfrak {g}）$，在可接受的级别$ k $ $ \ hat {\ Mathfrak {g}} $中，我们证明了弱$ v_k（\ Mathfrak {g}）的某些子类别（\ Mathfrak {g}）$ - 模块类别是emisimple的。结果，我们表明$ v_k（\ mathfrak {g}）$相对于一个Virasoro元素的家庭是理性的。我们还证明，对于Virasoro元素的家族，某些仿射顶点操作员超级级和最小$ W $ - 代数是合理的。
For the affine vertex algebra $V_k(\mathfrak{g})$ at an admissible level $k$ of $\hat{\mathfrak{g}}$, we prove that certain subcategory of weak $V_k(\mathfrak{g})$-module category is semisimple. As a consequence, we show that $V_k(\mathfrak{g})$ is rational with respect to a family of Virasoro elements. We also prove that certain affine vertex operator superalgebras and minimal $W$-algebras are rational with respect to a family of Virasoro elements.
