论文标题
关于$ \ Mathbb {C} $的合理性 - 分级顶点代数以及在共形流下的Weyl Vertex代数的应用
On rationality of $\mathbb{C}$-graded vertex algebras and applications to Weyl vertex algebras under conformal flow
论文作者
论文摘要
将朱代数用于特定类别的$ \ mathbb {c} $ - 分级顶点代数$ v $，我们证明，如果$ v $有限$ω$获得并满足合适的分级条件，那么$ v $，那么$ v $是理性的，即具有半含量的表示理论，具有半尺寸的zere zere zere zere zere zere zere zere zergra。在这里，$ω$表示$ v $中的向量通过降低分级的实际部分被歼灭。我们将结果应用于等级的一家Weyl顶点代数，具有共形元素$ω__$由$μ\ in \ mathbb {c} $参数化，并证明某些非直觉值的$μ$，这些顶点代数，这些dertex elgebras，它们是非智力级的，具有一个dimensiontion dimens zere zhue zhu的dimens zhuu。此外，我们将此结果推广到适当的$ \ mathbb {c} $ - 分级的weyl顶点代数的任意等级。
Using the Zhu algebra for a certain category of $\mathbb{C}$-graded vertex algebras $V$, we prove that if $V$ is finitely $Ω$-generated and satisfies suitable grading conditions, then $V$ is rational, i.e. has semi-simple representation theory, with one dimensional level zero Zhu algebra. Here $Ω$ denotes the vectors in $V$ that are annihilated by lowering the real part of the grading. We apply our result to the family of rank one Weyl vertex algebras with conformal element $ω_μ$ parameterized by $μ\in \mathbb{C}$, and prove that for certain non-integer values of $μ$, these vertex algebras, which are non-integer graded, are rational, with one dimensional level zero Zhu algebra. In addition, we generalize this result to appropriate $\mathbb{C}$-graded Weyl vertex algebras of arbitrary ranks.
