论文标题
排列的轨道和联想代数
Permutation orbifolds and associative algebras
论文作者
论文摘要
令$ v $为顶点操作员代数，$ g = \ left（1 \ 2 \ \ cdots k \ right）$是$ k $ cycle，被视为顶点操作员代数$ v^{\ otimes k} $的自动形态。事实证明，dong-li-mason的关联的关联代数$ a_ {g} \ left（v^{\ otimes k} \ right）$与Zhu的代数$ a \ a \ left（v \ right）$显式。该结果恢复了先前的结果，即不可约$ g $ twisted $ v^{\ otimes k} $ - 模块和不可减至的$ V $ -MODULES之间存在一对一的对应关系。
Let $V$ be a vertex operator algebra and $g=\left(1\ 2\ \cdots k\right)$ be a $k$-cycle which is viewed as an automorphism of the vertex operator algebra $V^{\otimes k}$. It is proved that Dong-Li-Mason's associated associative algebra $A_{g}\left(V^{\otimes k}\right)$ is isomorphic to Zhu's algebra $A\left(V\right)$ explicitly. This result recovers a previous result that there is a one-to-one correspondence between irreducible $g$-twisted $V^{\otimes k}$-modules and irreducible $V$-modules.
