Modular A(n)(V) theory
Modular A(n)(V) theory
复制标题
模 A(n)(V) 理论
DOI：
10.1016/j.jalgebra.2017.04.027
复制
发表时间：
2017
影响因子：
0.9
通讯作者：
L. Ren
中科院分区：
文献类型：
--
作者：
L. Ren
构造了任意代数闭域上顶点算子代数V与非负整数n的一系列结合代数An(V)，使得非An−1(V)模的不可约An(V)-模与不可约V-模一一对应.证明了V是有理的当且仅当An(V)对所有n都是半单的，特别地，任何不可约V-模的齐次子空间对有理顶点算子代数V都是有限维的。
A series of associative algebras A n (V) for a vertex operator algebra V over an arbitrary algebraically closed field and nonnegative integers n are constructed such that there is a one to one correspondence between irreducible A n (V)-modules which are not A n− 1 (V) modules and irreducible V-modules. Moreover, it is proved that V is rational if and only if A n (V) are semisimple for all n. In particular, the homogeneous subspaces of any irreducible V-module are finite dimensional for rational vertex operator algebra V.